A351724 Number of compositions of n into parts of size 1, 5, 10 or 25.

1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 9, 13, 18, 24, 31, 42, 58, 80, 109, 146, 197, 268, 366, 499, 676, 916, 1243, 1690, 2299, 3122, 4237, 5751, 7811, 10614, 14418, 19580, 26587, 36106, 49043, 66614, 90473, 122869, 166866, 226632, 307810, 418060, 567784, 771122, 1047296, 1422396, 1931845

Offset

0,6

Comments

Starts to differ from A114044 at n=50.

Links

Table of n, a(n) for n=0..50.

Index entries for sequences related to making change.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f. : 1/(1-x-x^5-x^10-x^25).

a(n) = +a(n-1) +a(n-5) +a(n-10) +a(n-25).

Example

a(8)=5 counts 5 compositions 1+1+1+1+1+1+1+1 = 1+1+1+5 = 1+1+5+1 = 1+5+1+1 = 5+1+1+1.

Crossrefs

Cf. A114044 (parts 50 and 100 admitted), A001299 (partitions).

Row sums of A351726.

Sequence in context: A255362 A017833 A114044 * A113444 A228669 A308020

Adjacent sequences: A351721 A351722 A351723 * A351725 A351726 A351727

Keyword

nonn,easy

Author

R. J. Mathar, Feb 17 2022

Status

approved