A029152 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^9)).

1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 3, 4, 7, 4, 7, 9, 7, 9, 14, 9, 14, 17, 14, 17, 24, 17, 24, 29, 24, 29, 38, 29, 38, 45, 38, 45, 57, 45, 57, 66, 57, 66, 81, 66, 81, 93, 81, 93, 111, 93, 111, 126, 111, 126, 148, 126, 148, 166, 148, 166, 192, 166, 192, 214, 192, 214, 244, 214, 244, 270, 244, 270, 305, 270, 305, 335, 305, 335, 375

Offset

0,7

Comments

a(n) is the number of partitions of n into parts 2, 3, 6, and 9. - Joerg Arndt, Aug 27 2025

Links

Table of n, a(n) for n=0..78.

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

Formula

a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=3, a(7)=1, a(8)=3, a(9)=4, a(10)=3, a(11)=4, a(12)=7, a(13)=4, a(14)=7, a(15)=9, a(16)=7, a(17)=9, a(18)=14, a(19)=9, a(n) = a(n-2)+a(n-3)-a(n-5)+a(n-6)-a(n-8)-a(n-12)+a(n-14)-a(n-15)+a(n-17)+a(n-18)-a(n-20). - Harvey P. Dale, Feb 20 2012

a(n) = floor((n^3+24*n^2+192*n+1944)/1944 + (n^2+20*n)*((n+2) mod 3)/324 - (n+5)*(n mod 2)/24 - n*((2*n^2+n) mod 3)/162). - Hoang Xuan Thanh, Oct 03 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^6)(1-x^9)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, -1, 1, 0, -1, 0, 0, 0, -1, 0, 1, -1, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 3, 4, 7, 4, 7, 9, 7, 9, 14, 9}, 60] (* Harvey P. Dale, Feb 20 2012 *)

Prog

(PARI) a(n) = (n^3+24*n^2+192*n+1944 + (6*n^2+120*n)*((n+2)%3) - 81*(n+5)*(n%2) - 12*n*((2*n^2+n)%3))\1944 \\ Hoang Xuan Thanh, Oct 03 2025

Crossrefs

Sequence in context: A296955 A219525 A050121 * A320279 A175290 A393449

Adjacent sequences: A029149 A029150 A029151 * A029153 A029154 A029155

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved