A352529 -id:A352529 - cp's OEIS frontend

A352530 Expansion of 1/Sum_{k>=0} x^(k^5).

1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 0, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -30, 31, -31, 30, -28, 25, -21, 16, -10, 3, 5, -14, 24, -35, 47, -60, 74, -89, 105, -122

Offset: 0

Seiichi Manyama, Mar 19 2022

sign

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000584, A317665, A323633, A352529.

my(N=99, x='x+O('x^N)); Vec(1/sum(k=0, N^(1/5), x^k^5))

a(n) = if(n==0, 1, -sum(k=1, n, ispower(k, 5)*a(n-k)));

A363748 Number of compositions into sums of fourth powers.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 22, 26, 31, 37, 44, 52, 61, 71, 82, 94, 107, 121, 136, 152, 169, 188, 210, 236, 267, 304, 348, 400, 461, 532, 614, 708, 815, 936, 1072, 1224, 1393, 1581, 1791, 2027, 2294, 2598, 2946, 3346, 3807, 4339, 4953, 5661, 6476, 7412, 8484, 9708, 11101, 12682, 14474

Offset: 0

Seiichi Manyama, Jun 19 2023

nonn

This sequence is different from A291149.

			a(18)=4 counts the compositions 1^4+1^4+1^4+2^4 = 1^4+1^4+2^4+1^4 = 1^4+2^4+1^4+1^4 = 2^4+1^4+1^4+1^4. - _R. J. Mathar_, Jun 21 2023

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A006456, A023358, A363749.

Cf. A000583, A291149, A352529.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, ispower(j, 4)*v[i-j+1])); v;

G.f.: 1/(1 - Sum_{k>=1} x^(k^4)).

cp's OEIS Frontend

A352530 Expansion of 1/Sum_{k>=0} x^(k^5).

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A363748 Number of compositions into sums of fourth powers.

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