A363748 Number of compositions into sums of fourth powers.

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

Author

Seiichi Manyama, Jun 19 2023

Keywords

• nonn

Comments

This sequence is different from A291149.

Examples

			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
		

Links

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

Crossrefs

Cf. A006456, A023358, A363749.

Cf. A000583, A291149, A352529.

Programs

PARI

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;

Formula

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