A029150 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^7)).

1, 0, 1, 1, 1, 1, 3, 2, 3, 4, 4, 4, 7, 6, 8, 9, 10, 10, 14, 13, 16, 18, 19, 20, 25, 24, 28, 31, 33, 34, 41, 40, 45, 49, 52, 54, 62, 62, 68, 73, 77, 80, 90, 90, 98, 104, 109, 113, 125, 126, 135, 143, 149, 154, 168, 170, 181

Offset

0,7

Comments

Number of partitions of n into parts 2, 3, 6, and 7. - Joerg Arndt, Aug 13 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1,1,1,-1,-2,-1,1,1,-1,0,1,1,0,-1).

Formula

a(n) = floor((n^3+27*n^2+306*n+1512)/1512 - (n+9)*(n mod 2)/24 - n*((n^2) mod 3)/18). - Hoang Xuan Thanh, Oct 02 2025

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^3) (1 - x^6) (1 - x^7)), {x, 0, 100}], x] (* Vincenzo Librandi, Aug 13 2013 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^7))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
(PARI) a(n) = (n^3+27*n^2+306*n+1512 - 63*(n+9)*(n%2) - 84*n*((n^2)%3))\1512 \\ Hoang Xuan Thanh, Oct 02 2025
(Magma) m:=80; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^7)))); // Vincenzo Librandi, Aug 13 2013

Crossrefs

Sequence in context: A077070 A374560 A075988 * A255246 A055923 A035634

Adjacent sequences: A029147 A029148 A029149 * A029151 A029152 A029153

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved