A376630 G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^(2*j-1)).

1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 2, 2, 1, 1, 2, 3, 2, 1, 3, 2, 2, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 5, 5, 5, 4, 4, 7, 7, 5, 6, 8, 7, 7, 6, 8, 10, 8, 8, 10, 11, 9, 10, 12, 12, 11, 12, 14, 14, 13, 13, 16, 17, 15, 17, 18, 18, 19, 19, 20, 21, 22, 22, 24, 24, 25, 26, 27, 28, 29, 30

Offset

0,7

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

G.f.: Sum_{k>=0} Product_{j=1..k} (x^j + x^(3*j-1)).

a(n) ~ c * A376660^sqrt(n) / sqrt(n), where c = sqrt(cosh(arccosh(sqrt(31)/2) / 3))/31^(1/4) = 0.456748282933947534736955792823221857...

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2)*Product[1+x^(2*j-1), {j, 1, k}], {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k - 1))*x^k]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p; , {k, 1, Sqrt[2*nmax]}]; Take[CoefficientList[s, x], nmax + 1]

Crossrefs

Cf. A000009, A053258, A053261, A333179, A376629, A376660.

Sequence in context: A029368 A108483 A363623 * A101565 A377404 A292944

Adjacent sequences: A376627 A376628 A376629 * A376631 A376632 A376633

Keyword

nonn

Author

Vaclav Kotesovec, Sep 30 2024

Status

approved