A348310 a(n) = Sum_{k=0..floor(n/10)} (-1)^k * binomial(n-5*k,5*k).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, -5, -20, -55, -125, -251, -461, -791, -1286, -2001, -3001, -4356, -6121, -8281, -10626, -12500, -12340, -6885, 10110, 49875, 131626, 286921, 565781, 1044971, 1838626, 3110751, 5087561, 8064366, 12395461, 18444251, 26451625, 36249035, 46692715, 54618710

Offset: 0

Author

Seiichi Manyama, Oct 11 2021

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1,0,0,0,0,-1).

Crossrefs

Cf. A348308, A348309.

Cf. A289306, A348290.

Programs

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 45] (* Amiram Eldar, Oct 11 2021 *)

PARI

a(n) = sum(k=0, n\10, (-1)^k*binomial(n-5*k, 5*k));

PARI

my(N=66, x='x+O('x^N)); Vec((1-x)^4/((1-x)^5+x^10))

Formula

G.f.: (1-x)^4/((1-x)^5 + x^10).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) - a(n-10).