A377300 G.f.: Sum_{k>=1} k * x^(k*(7*k - 7 + 2)/2) / (1 - x^k).

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 4, 3, 1, 6, 1, 3, 4, 3, 1, 6, 1, 3, 4, 3, 1, 6, 1, 3, 4, 3, 1, 6, 5, 3, 4, 3, 5, 6, 1, 3, 8, 3, 1, 6, 5, 3, 4, 3, 5, 6, 1, 3, 8, 3, 1, 6, 5, 3, 4, 3, 5, 11, 1, 3, 8, 3, 6, 6, 5, 3, 4, 8, 5, 6, 1, 3, 13

Offset

1,9

Comments

In general, for d > 0, if g.f. = Sum_{k>=1} k * x^(k*(d*k - d + 2)/2) / (1 - x^k), then Sum_{k=1..n} a(k) ~ 2^(3/2) * n^(3/2) / (3*sqrt(d)).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

Sum_{k=1..n} a(k) ~ 2^(3/2) * n^(3/2) / (3*sqrt(7)).

Mathematica

Table[Sum[If[n > 7*k*(k-1)/2 && IntegerQ[n/k - 7*(k-1)/2], k, 0], {k, Divisors[2*n]}], {n, 1, 100}]
nmax = 100; Rest[CoefficientList[Series[Sum[k*x^(k*(7*k - 7 + 2)/2)/(1 - x^k), {k, 1, Sqrt[2*nmax/7] + 1}], {x, 0, nmax}], x]]

Crossrefs

Column 7 of A334466.

Sequence in context: A176040 A125768 A377301 * A334949 A334732 A266875

Adjacent sequences: A377297 A377298 A377299 * A377301 A377302 A377303

Keyword

nonn

Author

Vaclav Kotesovec, Oct 23 2024

Status

approved