A392356 - OEIS

%I #17 Jan 08 2026 14:55:52

%S 1,0,1,0,1,0,1,0,1,1,1,6,1,21,1,56,1,126,2,252,12,462,67,792,287,1287,

%T 1002,2003,3004,3019,8009,4504,19449,7004,43759,12444,92380,27132,

%U 184778,69768,352948,190893,648418,516648,1154693,1341154,2014387,3311290

%N a(n) = Sum_{k=0..floor(5*n/9)} binomial(k,5*n-9*k).

%H Seiichi Manyama, <a href="/A392356/b392356.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-10,0,10,0,-5,1,1).

%F G.f.: (1-x^2)^4 / ((1-x^2)^5 - x^9).

%F a(n) = 5*a(n-2) - 10*a(n-4) + 10*a(n-6) - 5*a(n-8) + a(n-9) + a(n-10).

%t CoefficientList[Series[(1-x^2)^4/((1-x^2)^5-x^9),{x,0,60}],x] (* _Vincenzo Librandi_, Jan 08 2026 *)

%o (PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)^4/((1-x^2)^5-x^9))

%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-x^2)^4 / ((1-x^2)^5 - x^9)); // _Vincenzo Librandi_, Jan 08 2026

%Y Cf. A392271, A392355.

%K nonn,easy

%O 0,12

%A _Seiichi Manyama_, Jan 08 2026