A390040 - OEIS

%I #22 Jan 16 2026 10:43:36

%S 1,0,4,0,10,0,20,0,35,1,56,8,84,36,120,120,165,330,221,792,298,1716,

%T 442,3432,819,6435,1925,11441,5048,19464,13192,31960,32793,51204,

%U 76722,81396,169291,131784,354276,224808,707413,415701,1355642,836418,2507299

%N a(n) = Sum_{k=0..floor(n/2)} binomial(k+3,4*n-8*k+3).

%H Seiichi Manyama, <a href="/A390040/b390040.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1,1).

%F G.f.: 1 / ((1-x^2)^4 - x^9).

%F a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8) + a(n-9).

%t CoefficientList[Series[1/((1-x^2)^4-x^9),{x,0,60}],x] (* _Vincenzo Librandi_, Jan 16 2026 *)

%o (PARI) my(N=50, x='x+O('x^N)); Vec(1/((1-x^2)^4-x^9))

%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1 / ((1-x^2)^4 - x^9)); // _Vincenzo Librandi_, Jan 16 2026

%Y Cf. A390042.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Jan 14 2026