A054355 Binomial transform of Kolakoski sequence A000002.

1, 3, 7, 14, 26, 48, 91, 178, 357, 728, 1497, 3083, 6331, 12937, 26292, 53144, 106846, 213676, 425126, 841854, 1660587, 3266550, 6416933, 12607706, 24811601, 48969428, 97010347, 192968489, 385347506, 772039743, 1550372341, 3117282657

Offset

0,2

Comments

Before taking the transform, relabel A000002 so the subscripts start at 0 instead of 1.

Links

Table of n, a(n) for n=0..31.

Maple

# Using R. J. Mathar's function A000002.
binomial_transform := (sq, dim) -> local n, k; seq(add(binomial(n, k) * sq(k), k = 0..n), n = 0..dim):
binomial_transform(n -> A000002(n + 1), 31);  # Peter Luschny, Jul 05 2026

Prog

(Python) # Using David Eppstein's Kolakoski function from A000002.
from typing import Iterator
def binomial_trans(seq: Iterator, dim: int) -> list[int]:
    c = []; t = []
    for _ in range(dim):
        try: r = next(seq)
        except StopIteration: break
        c += [r]
        for i in range(len(c) - 1, 0, -1):
            c[i - 1] += c[i]
        t.append(c[0])
    return t
A054355 = binomial_trans(Kolakoski(), 32); print(A054355)  # Peter Luschny, Jul 05 2026

Crossrefs

Cf. A000002.

Sequence in context: A132109 A317779 A099854 * A245268 A117071 A019459

Adjacent sequences: A054352 A054353 A054354 * A054356 A054357 A054358

Keyword

nonn

Author

N. J. A. Sloane, May 07 2000

Status

approved