A259714 a(n) = Sum_{k=1..n-1}((k mod 5)*a(n-k)), a(1) = 1.

1, 1, 3, 8, 21, 50, 129, 327, 827, 2089, 5290, 13386, 33868, 85693, 216836, 548660, 1388269, 3512737, 8888292, 22490049, 56906580, 143990771, 364339983, 921889753, 2332658401, 5902327520, 14934664284, 37789193522, 95618028007, 241942376384

Offset: 1

Author

Anders Hellström, Jul 03 2015

Keywords

• nonn

Links

• Anders Hellström, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A088305 (sequence obtained without mod 5 in the formula).

Programs

Mathematica

f[n_] := Block[{k, a = {1}}, Do[AppendTo[a, Sum[Mod[k, 5] a[[i - k]], {k, 1, i - 1}]], {i, 2, n}]; a]; f@ 30 (* Michael De Vlieger, Jul 03 2015 *)

PARI

main(size)=my(v=vector(size),n,s); v[1]=1; for(n=2, size, for(s=1, n-1, v[n] = v[n] + (s%5)*v[n-s] )); v;

Formula

Conjectures from Colin Barker, Jul 04 2015: (Start)

a(n) = a(n-1)+2*a(n-2)+3*a(n-3)+4*a(n-4)+a(n-5) for n>6.

G.f.: x*(x-1)*(x^4+x^3+x^2+x+1) / ((x+1)*(x^4+3*x^3+2*x-1)).

(End)