A372304 Binomial transform of the Gray code sequence.

0, 1, 5, 14, 36, 92, 228, 536, 1200, 2608, 5624, 12224, 26920, 59824, 133024, 293504, 638816, 1367488, 2877728, 5962112, 12198000, 24748192, 50041312, 101366272, 206655440, 425423136, 885598720, 1863228544, 3953671808, 8436151552, 18042976640, 38567833600

Offset

0,3

Comments

Also second binomial transform of A109629.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3311

Wikipedia, Gray code

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A003188(k).

Maple

g:= proc(n) g(n):= Bits[Xor](n, iquo(n, 2)) end:
a:= n-> add(binomial(n, k)*g(k), k=0..n):
seq(a(n), n=0..40);

Prog

(Python)
from math import comb
def A372304(n): return sum(comb(n, k)*(k^k>>1) for k in range(n+1)) # Chai Wah Wu, May 02 2024

Crossrefs

Cf. A003188, A109629.

Sequence in context: A097507 A052951 A048745 * A307462 A292170 A224716

Adjacent sequences: A372300 A372301 A372302 * A372307 A372308 A372309

Keyword

nonn

Author

Alois P. Heinz, May 02 2024

Status

approved