A376723 - OEIS

%I #13 Oct 03 2024 13:22:13

%S 1,0,2,2,3,10,7,28,33,64,132,170,408,578,1119,2002,3194,6310,10021,

%T 18666,32353,55450,101443,170672,308744,534820,935936,1663892,2872669,

%U 5111652,8898082,15641802,27538647,48049562,84813451,148219128,260572901,457451088

%N Expansion of 1/((1 - x^2 - x^3)^2 - 4*x^5).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,2,-1).

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

%F a(n) = (1/2) * Sum_{k=0..floor(n/2)} binomial(2*k+2,2*n-4*k+1).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x^2-x^3)^2-4*x^5))

%o (PARI) a(n) = sum(k=0, n\2, binomial(2*k+2, 2*n-4*k+1))/2;

%Y Cf. A182890, A376724, A376725.

%Y Cf. A376726, A376729.

%Y Cf. A375278.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 02 2024