A029051 Expansion of 1/((1-x)(1-x^3)(1-x^7)(1-x^10)).

1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 7, 7, 8, 10, 11, 12, 14, 16, 17, 19, 22, 24, 26, 29, 32, 34, 37, 41, 44, 47, 52, 56, 59, 64, 69, 73, 78, 84, 89, 94, 101, 107, 113, 120, 127, 134, 141, 149, 157, 165, 174, 183, 192, 201, 211

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 7 and 10. - Ilya Gutkovskiy, May 14 2017

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=2, a(6)=3, a(7)=4, a(8)=4, a(9)=5, a(10)=7, a(11)=7, a(12)=8, a(13)=10, a(14)=11, a(15)=12, a(16)=14, a(17)=16, a(18)=17, a(19)=19, a(20)=22, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-7)-a(n-8)- a(n-13)+ a(n-14)-a(n-17)+a(n-18)+a(n-20)-a (n-21). - Harvey P. Dale, May 06 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^7)(1-x^10)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 1, -1}, {1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 7, 7, 8, 10, 11, 12, 14, 16, 17, 19, 22}, 70] (* Harvey P. Dale, May 06 2013 *)

Prog

(PARI) a(n)=floor((2*n^3+63*n^2+582*n+2456)/2520+2*((n%10<1)-(n%10>8))/5+(n+1)%3/9) \\ Tani Akinari, May 31 2014

Crossrefs

Sequence in context: A077564 A088044 A351908 * A338826 A274201 A079398

Adjacent sequences: A029048 A029049 A029050 * A029052 A029053 A029054

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved