A029432 Expansion of 1/((1-x^7)*(1-x^8)*(1-x^9)*(1-x^10)).

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 18, 18, 19, 19, 20, 20, 22, 22, 24, 24, 25, 25, 26, 27

Offset

0,17

Comments

a(n) is the number of partitions of n into parts 7, 8, 9, and 10. - Joerg Arndt, Jan 20 2025

Links

Table of n, a(n) for n=0..77.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-2,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,-1).

Formula

There is a lengthy linear recurrence that generates the terms of this sequence, but it requires 34 initial terms to be provided and it requires reference to 14 prior terms to calculate the next term. [Harvey P. Dale, Feb 21 2012]

Mathematica

CoefficientList[Series[1/((1-x^7)(1-x^8)(1-x^9)(1-x^10)), {x, 0, 80}], x] (* Harvey P. Dale, Feb 21 2012 *)

Crossrefs

Sequence in context: A241492 A227739 A047971 * A073426 A232439 A346118

Adjacent sequences: A029429 A029430 A029431 * A029433 A029434 A029435

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved