A385087 2-adic valuation of A039699.

3, 3, 10, 3, 6, 8, 12, 3, 6, 6, 11, 8, 11, 12, 16, 3, 6, 6, 12, 6, 9, 13, 17, 8, 11, 11, 16, 12, 15, 16, 20, 3, 6, 6, 14, 6, 9, 11, 15, 6, 9, 9, 14, 13, 16, 17, 21, 8, 11, 11, 17, 11, 14, 17, 21, 12, 15, 15, 20, 16, 19, 20, 24, 3, 6, 6, 13, 6, 9, 11, 15, 6, 9, 9, 14, 11, 14, 15, 19, 6

Offset

1,1

Links

Table of n, a(n) for n=1..80.

Nikolai Beluhov, Powers of 2 in High-Dimensional Lattice Walks, arXiv:2506.12789 [math.CO], 2025. See w4(n) in Table 1 p. 2.

Formula

a(n) = A007814(A039699(n)) = A000120(n) + A007814(A002895(n)).

Prog

(PARI) C=binomial;
A002895(n) = sum(k=0, n, C(n, k)^2 * C(2*n-2*k, n-k) * C(2*k, k) );
a(n) = hammingweight(n) + valuation(A002895(n), 2);
(Python)
from math import comb
def A385087(n): return (~(a:=(sum(comb(n, k)**2*comb(n-k<<1, n-k)*comb(m:=k<<1, k) for k in range(n+1>>1))<<1) + (0 if n&1 else comb(n, n>>1)**4)) & a-1).bit_length() + n.bit_count() # Chai Wah Wu, Jun 17 2025

Crossrefs

Cf. A000120, A002895, A007814, A039699.

Sequence in context: A072004 A095271 A054511 * A362469 A286570 A134704

Adjacent sequences: A385084 A385085 A385086 * A385088 A385089 A385090

Keyword

nonn,easy

Author

Michel Marcus, Jun 17 2025

Status

approved