A029011 Expansion of 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^6)).

1, 1, 2, 2, 3, 4, 6, 7, 9, 10, 13, 15, 19, 21, 25, 28, 33, 37, 43, 47, 54, 59, 67, 73, 82, 89, 99, 107, 118, 127, 140, 150, 164, 175, 190, 203, 220, 234, 252, 267, 287, 304, 326, 344, 367, 387, 412, 434, 461, 484, 513, 538, 569, 596, 629, 658, 693, 724, 761, 794

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of n into parts 1, 2, 5 and 6. - David Neil McGrath, Dec 06 2014

Number of walks (closed) on the graph G(1-vertex; 1-loop, 2-loop, 5-loop, 6-loop) where the order of loops is unimportant. - David Neil McGrath, Dec 06 2014

Examples

			There are 6 partitions of n=6 into parts 1, 2, 5 and 6. These are (6)(51)(222)(2211)(21111)(111111). - _David Neil McGrath_, Dec 06 2014
		

Links

• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1,0,-2,0,1,0,-1,1,1,-1).

Crossrefs

Cf. A029177(2*n) = a(n).

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^5)(1-x^6)),{x,0,60}],x]
LinearRecurrence[{1,1,-1,0,1,0,-2,0,1,0,-1,1,1,-1},{1,1,2,2,3,4,6,7,9,10,13,15,19,21},70] (* Harvey P. Dale, Dec 14 2020 *)

PARI

a(n)=if(n<-13,-a(-14-n),polcoeff(1/((1-x)*(1-x^2)*(1-x^5)*(1-x^6))+x*O(x^n),n))

Formula

G.f.: 1/((1-x)(1-x^2)(1-x^5)(1-x^6)).

a(n) = -a(-14-n).

a(n) = a(n-2) + a(n-5) + a(n-6) - a(n-7) - a(n-8) - a(n-11) + a(n-13) + 1.

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5) - 2*a(n-7) + a(n-9) - a(n-11) + a(n-12) + a(n-13) - a(n-14). - David Neil McGrath, Dec 06 2014

a(n) = 1 + [(n mod 30)=12] + floor((2n^3 + 42*n^2 + (261+15*(-1)^n)*n)/720). - Hoang Xuan Thanh, Jun 25 2025