A375275 Expansion of (1 - x + x^2)/(1 - 2*x + 3*x^2 + 2*x^3 + x^4).

1, 1, 0, -5, -13, -12, 25, 117, 196, 3, -841, -2200, -2079, 4121, 19720, 33435, 1547, -140772, -372775, -359763, 678796, 3323203, 5702319, 437200, -23557759, -63154959, -62213360, 111716475, 559940707, 972313668, 103585625, -3941367643, -10698060204

Offset: 0

Author

Seiichi Manyama, Aug 09 2024

Keywords

• sign

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-3,-2,-1).

Crossrefs

Cf. A108479, A108480, A108484.

Cf. A375255.

Programs

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))

PARI

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

Formula

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

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