A348290 a(n) = Sum_{k=0..floor(n/10)} binomial(n-5*k,5*k).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 22, 57, 127, 253, 463, 793, 1288, 2003, 3005, 4380, 6255, 8855, 12630, 18508, 28358, 45783, 77408, 134883, 237888, 418513, 727513, 1243163, 2083888, 3426771, 5535911, 8808206, 13850761, 21615771, 33638409, 52455339, 82332229, 130506914, 209273284

Offset: 0

Author

Seiichi Manyama, Oct 10 2021

Keywords

• nonn
• 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. A000045, A005252, A100134, A348289.

Programs

PARI

a(n) = sum(k=0, n\10, 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).