A029040 - OEIS

%I #17 Jan 18 2017 10:03:39

%S 1,1,1,2,2,3,4,4,6,7,8,10,11,13,15,17,20,22,25,28,31,35,38,42,47,51,

%T 56,61,66,72,78,84,91,98,105,113,121,129,138,147,157,167,177,188,199,

%U 211,223,235,249,262,276,291,305

%N Expansion of 1/((1-x)(1-x^3)(1-x^5)(1-x^8)).

%C a(n) is the number of partitions of n into parts 1, 3, 5, and 8. - _Joerg Arndt_, Jan 18 2017

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,1,-1,0,0,0,0,-1,1,-1,1,0,1,-1).

%F G.f.: 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^8)).

%F a(n) = floor((2*n^3+51*n^2+384*n+1368+180*(1+(-1)^floor((n+1)/2))*(-1)^floor(n/4))/1440). - _Tani Akinari_, Jun 28 2013

%t CoefficientList[Series[1/((1 - x) (1 - x^3) (1 - x^5) (1 - x^8)), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Jan 17 2017 *)

%o (PARI) a(n)=(2*n^3+51*n^2+384*n+1368+(1+(-1)^((n+1)\2))*(-1)^(n\4)*180)\1440 \\ _Charles R Greathouse IV_, Jun 28 2013

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_