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

0,17

Comments

This sequence is different from A291149.

Links

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

Formula

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

Example

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

Prog

(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;

Crossrefs

Cf. A006456, A023358, A363749.

Cf. A000583, A291149, A352529.

Sequence in context: A247759 A247752 A291149 * A322463 A275156 A188459

Adjacent sequences: A363745 A363746 A363747 * A363749 A363750 A363751

Keyword

nonn

Author

Seiichi Manyama, Jun 19 2023

Status

approved