A029047 Expansion of 1/((1-x)(1-x^3)(1-x^6)(1-x^10)).

1, 1, 1, 2, 2, 2, 4, 4, 4, 6, 7, 7, 10, 11, 11, 14, 16, 16, 20, 22, 23, 27, 30, 31, 36, 39, 41, 46, 50, 52, 59, 63, 66, 73, 78, 81, 90, 95, 99, 108, 115, 119, 130, 137, 142, 153, 162, 167, 180, 189, 196, 209, 220, 227, 242, 253, 262, 277, 290, 299, 317, 330

Offset

0,4

Comments

Number of partitions of n into the first four triangular numbers, 1, 3, 6 and 10.

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,-1,0,1,-1,0,-1,2,-1,0,-1,1,0,-1,1,0,1,-1).

Maple

M:= Matrix(20, (i, j)-> if (i=j-1) or (j=1 and member(i, [1, 3, 6, 14, 17, 19])) then 1 elif j=1 and member(i, [4, 7, 9, 11, 13, 16, 20]) then -1 elif j=1 and i=10 then 2 else 0 fi): a:= n-> (M^(n))[1, 1]: seq(a(n), n=0..80); # Alois P. Heinz, Jul 25 2008

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^6)(1-x^10)), {x, 0, 70}], x] (* Harvey P. Dale, Feb 06 2020 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^3)*(1-x^6)*(1-x^10))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
(PARI) a(n)=floor((2*n^3+60*n^2+527*n+1243+9*(n+1)*(-1)^n+(120*(n\3+1)*[1, 1, -2]+20*[61, 41, 0])[n%3+1])/2160) \\ Tani Akinari, May 07 2014

Crossrefs

Cf. A008620.

Sequence in context: A086159 A029048 A086160 * A007294 A053282 A218084

Adjacent sequences: A029044 A029045 A029046 * A029048 A029049 A029050

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved