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

0,3

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

Links

Table of n, a(n) for n=0..59.

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).

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

Example

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

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 *)

Prog

(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))

Crossrefs

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

Sequence in context: A039859 A130291 A067835 * A077117 A237976 A035365

Adjacent sequences: A029008 A029009 A029010 * A029012 A029013 A029014

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved