A094909 Let p_k(n) = number of partitions of n into exactly k parts; sequence gives p_3(n-3) + p_2(n-2) + 1.

1, 1, 1, 1, 2, 2, 4, 4, 6, 7, 9, 10, 13, 14, 17, 19, 22, 24, 28, 30, 34, 37, 41, 44, 49, 52, 57, 61, 66, 70, 76, 80, 86, 91, 97, 102, 109, 114, 121, 127, 134, 140, 148, 154, 162, 169, 177, 184, 193, 200, 209, 217, 226, 234, 244, 252, 262, 271, 281, 290, 301, 310, 321

Offset: 0

Author

N. J. A. Sloane, Jun 18 2004

Keywords

• nonn
• easy

Links

• S. L. Devadoss, Combinatorial equivalence of real moduli spaces, Notices Amer. Math. Soc., 51 (No. 6, 2004), 620-628 (see Cor. 7).
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).

Crossrefs

p_k(n) = A008284(n,k).

Programs

PARI

Vec((x^7-x^6-x^5-x^4+x^3+x^2-1)/((1+x)*(x^2+x+1)*(x-1)^3) + O(x^80)) \\ Michel Marcus, Jul 19 2015

Formula

G.f.: (x^7-x^6-x^5-x^4+x^3+x^2-1)/((1+x)*(x^2+x+1)*(x-1)^3). - Alois P. Heinz, Jul 19 2015

72*a(n) = 8*A099837(n+3) +27*(-1)^n +29 +6*n^2, (n>1). - R. J. Mathar, Nov 15 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 19 2015