A029314 - OEIS

%I #11 Apr 12 2026 08:41:08

%S 1,0,0,1,0,0,1,1,0,1,2,0,2,2,1,2,2,2,2,3,3,3,4,3,5,4,4,6,5,5,7,7,6,8,

%T 9,7,10,10,9,11,12,11,13,14,13,15,16,15,18,18,18,20,21,20,23,24,23,26,

%U 27,26,30,30,30,33,34,33,37

%N Expansion of 1/((1-x^3)*(1-x^7)*(1-x^10)*(1-x^12)).

%C Number of partitions of n into parts 3, 7, 10, and 12. - _Hoang Xuan Thanh_, Apr 12 2026

%H <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,0,0,1,0,0,0,0,1,-1,0,-1,0,-1,0,-1,1,0,0,0,0,1,0,0,0,1,0,0,-1).

%F a(n) = floor((n^3+48*n^2+864*n+1134)/15120 - (n mod 2)*(n+114)/240 - ((2*n^2+n) mod 3)*n/36 + ((5*n^3+2*n^2+n+1) mod 7)/7 + (1-(floor(n/5) mod 2))*((n^4+4*n^3+2*n^2+n+4) mod 5)/5 + (floor(n/5) mod 2)*((4*n^4+3*n^3+4*n^2+4*n+2) mod 5)/5). - _Hoang Xuan Thanh_, Apr 12 2026

%t CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^10)(1-x^12)), {x, 0, 100}], x] (* _Jinyuan Wang_, Mar 12 2020 *)

%o (PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^10)*(1-x^12)) + O(x^50)) \\ _Hoang Xuan Thanh_, Apr 12 2026

%K nonn,easy

%O 0,11

%A _N. J. A. Sloane_