A029361 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^8)*(1-x^11)).

1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 1, 3, 3, 0, 2, 4, 3, 1, 4, 5, 4, 2, 5, 6, 5, 4, 7, 7, 7, 6, 8, 9, 9, 8, 10, 11, 12, 10, 12, 14, 15, 12, 15, 17, 18, 15, 18, 21, 21, 18, 22, 25, 25, 22, 26, 29, 29, 26, 31, 34, 34, 31, 36

Offset

0,9

Comments

Number of partitions of n into parts from {4,7,8,11}. Example: a(15)=3 because we have [11,4],[8,7] and [7,4,4]. - Emeric Deutsch, Mar 06 2006

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((n+43)*(n^2+2*n+180)/14784 - (n mod 2)*n/64 + ((n^3+2*n+1) mod 4)*n/32 - (15*((n^3+n^2) mod 4) + 9*((n^3+3*n) mod 4))/32 + (((5*n^3+5*n^2+10*n+10) mod 11) + ((n+5) mod 11) - ((n+4) mod 11) - ((n+3) mod 11) + ((n+2) mod 11))/11). - Hoang Xuan Thanh, May 15 2026

Maple

g:=1/(1-x^4)/(1-x^7)/(1-x^8)/(1-x^11): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..66); # Emeric Deutsch, Mar 06 2006

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^8)(1-x^11)), {x, 0, 70}], x] (* Harvey P. Dale, Mar 02 2019 *)

Crossrefs

Sequence in context: A230994 A337509 A144734 * A275966 A284059 A329767

Adjacent sequences: A029358 A029359 A029360 * A029362 A029363 A029364

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved