A392271 - OEIS

%I #20 Jan 07 2026 04:22:40

%S 1,0,1,0,1,1,1,4,1,10,2,20,8,35,29,57,85,94,211,175,464,385,938,935,

%T 1808,2289,3459,5385,6826,12031,14198,25686,30960,53176,69143,108699,

%U 154433,223215,340006,465867,734561,991088,1561313,2138884,3286129,4643816,6900097,10067197

%N a(n) = Sum_{k=0..floor(3*n/5)} binomial(k,3*n-5*k).

%H Seiichi Manyama, <a href="/A392271/b392271.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,1,1).

%F G.f.: (1-x^2)^2 / ((1-x^2)^3 - x^5).

%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-5) + a(n-6).

%F a(2*n) = A107025(n), a(2*n+1) = A373963(n+1).

%t CoefficientList[Series[(1-x^2)^2/((1-x^2)^3-x^5),{x,0,60}],x] (* _Vincenzo Librandi_, Jan 07 2026 *)

%o (PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)^2/((1-x^2)^3-x^5))

%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1-x^2)^2 / ((1-x^2)^3 - x^5)); // _Vincenzo Librandi_, Jan 07 2026

%Y Cf. A003522, A392253, A392272, A392273.

%Y Cf. A017837, A107025, A373963.

%K nonn

%O 0,8

%A _Seiichi Manyama_, Jan 05 2026