We have the numbers with different colours with the sequence: ['red', 'yellow', 'blue'].

That sequence colours the numbers in the following way:

 1   2   3    4    5   6  7   8   9   10   11  12   13 .....

We have got the following recursive function:

  ```
f(1) = 1
f(n) = f(n - 1) + n
```

Some terms of this sequence with their corresponding colour are:

```
term   value   colour
1        1     "red"
2        3     "blue"
3        6     "blue"
4       10     "red"
5       15     "blue"
6       21     "blue"
7       28     "red"
```

The three terms of the same colour "blue", higher than 3, are: `[6, 15, 21]`

We need a function `same_col_seq(), that may receive three arguments:

- `val`, an integer number
- `k`, an integer number
- `colour`, the name of one of the three colours(red, yellow or blue), as a string.

The function will output a sorted array with the smallest `k` terms, having the same marked colour, but higher than `val`.

Let's see some examples:

```python
same_col_seq(3, 3, 'blue') == [6, 15, 21]
same_col_seq(100, 4, 'red') == [136, 190, 253, 325]
```

The function may output an empty list if it does not find terms of the sequence with the wanted colour in the range [val, 2* k * val]

```python
same_col_seq(250, 6, 'yellow') == []
```

That means that the function did not find any "yellow" term in the range `[250, 3000]`
 
Tests will be with the following features:

* Nmber of tests: `100`
* `100 < val < 1000000`
* `3 < k < 20`

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "def same_col_seq(val, k, col):\n    # your code here\n    code ={'blue':0,'red':1,'yellow':2}\n    result =[]\n    limit = 2 * k * val   \n    term  =  1\n    temp  =  1\n    while(temp <= val):\n        temp =  temp + term + 1\n        term +=1\n        \n    while(True):\n        if(temp % 3  == code[col]):\n            result.append(temp)\n        temp = temp + term + 1\n        term +=1\n        \n        if(len(result)>= k  ):\n            break\n        if(len(result) == 0 and temp>=limit):\n            return []   \n\n    return result"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'same_col_seq'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5888