A029341 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^9)*(1-x^10)).

1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 1, 2, 3, 2, 1, 2, 4, 4, 4, 2, 4, 5, 6, 5, 4, 6, 8, 8, 8, 6, 9, 10, 11, 10, 10, 12, 14, 14, 15, 13, 16, 17, 19, 19, 18, 20, 23, 24, 25, 22, 26, 28, 31, 30, 29, 32, 36, 37, 38, 35, 40, 43, 46, 45, 44, 48, 53, 54, 55, 52, 59, 62, 65, 64, 64, 69, 74, 75

Offset

0,10

Comments

Number of partitions of n into parts 4, 5, 9, and 10. - Hoang Xuan Thanh, Apr 25 2026

Links

Table of n, a(n) for n=0..79.

Index entries for two-way infinite sequences

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

Formula

G.f.: 1/((1-x^4)(1-x^5)(1-x^9)(1-x^10)).

a(n) = a(n-4)+a(n-5)+a(n-10)-a(n-13)-2*a(n-14)-a(n-15)+a(n-18)+a(n-23)+a(n-24)-a(n-28) = -a(-28-n).

a(n) = floor((n^3+42*n^2+168*n+864)/10800 - (n mod 2)*(n-4)/80 + ((2*n^2+n+2) mod 5)*n/50 - (n mod 3)/27 - ((n^3+n^2+2*n) mod 4)/8 + (3*((n^4+n+3) mod 5) + ((4*n^4+2*n^3+n^2+3*n) mod 5))/10 + ((2*n^3+2*n^2+1) mod 5)/50). - Hoang Xuan Thanh, Apr 25 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^9)(1-x^10)), {x, 0, 90}], x] (* Harvey P. Dale, Dec 01 2015 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, -1, -2, -1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 1, 2, 3, 2, 1, 2, 4, 4, 4, 2, 4, 5, 6, 5, 4, 6, 8}, 90] (* Harvey P. Dale, Dec 01 2015 *)

Prog

(PARI) a(n)=if(n<-27, -a(-28-n), if(n<0, 0, polcoeff(1/((1-x^4)*(1-x^5)*(1-x^9)*(1-x^10))+x*O(x^n), n)))

Crossrefs

Sequence in context: A292944 A327188 A330270 * A240181 A079070 A354787

Adjacent sequences: A029338 A029339 A029340 * A029342 A029343 A029344

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved