A375275 - OEIS

%I #11 Aug 09 2024 10:07:33

%S 1,1,0,-5,-13,-12,25,117,196,3,-841,-2200,-2079,4121,19720,33435,1547,

%T -140772,-372775,-359763,678796,3323203,5702319,437200,-23557759,

%U -63154959,-62213360,111716475,559940707,972313668,103585625,-3941367643,-10698060204

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,-2,-1).

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

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

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

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

%Y Cf. A108479, A108480, A108484.

%Y Cf. A375255.

%K sign

%O 0,4

%A _Seiichi Manyama_, Aug 09 2024