A375273 - OEIS

%I #11 Aug 09 2024 10:07:37

%S 1,2,7,24,73,238,763,2436,7821,25050,80255,257200,824081,2640582,

%T 8461187,27111644,86872853,278363058,891946503,2858027016,9157854361,

%U 29344123550,94026132235,301283944500,965391362461,3093362593162,9911930522767,31760378496864

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,4,-4).

%F a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-2*x-3*x^2-4*x^3+4*x^4))

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

%Y Cf. A182890, A375255.

%Y Cf. A108480, A108488.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 09 2024