A029042 - OEIS

A029042

Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^10)).

1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 19, 22, 24, 28, 31, 33, 37, 40, 45, 49, 52, 57, 61, 68, 73, 77, 84, 89, 97, 104, 109, 117, 124, 134, 142, 149, 159, 167, 179, 189, 197, 209, 219, 233, 245, 255, 269, 281, 297, 311, 323, 339, 353, 372, 388

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OFFSET

0,4

COMMENTS

Number of partitions of n into parts 1, 3, 5 and 10. - Ilya Gutkovskiy, May 14 2017

LINKS

Table of n, a(n) for n=0..61.

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

FORMULA

a(n) = floor((2*n^3 + 57*n^2 + 438*n + 1800)/1800 + (n/50) *(((n+1)*(2-n)) mod 5) ). - Hoang Xuan Thanh, Sep 07 2025

MATHEMATICA

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^5)(1-x^10)), {x, 0, 100}], x] (* or *) LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1, 1, -1, 0, -1, 1, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 19, 22}, 100] (* Harvey P. Dale, Mar 31 2025 *)

CROSSREFS

Sequence in context: A390488 A324744 A097920 * A320470 A320382 A259200

Adjacent sequences: A029039 A029040 A029041 * A029043 A029044 A029045

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved