%I #23 Jul 19 2015 13:45:34
%S 1,1,3,8,21,50,129,327,827,2089,5290,13386,33868,85693,216836,548660,
%T 1388269,3512737,8888292,22490049,56906580,143990771,364339983,
%U 921889753,2332658401,5902327520,14934664284,37789193522,95618028007,241942376384
%N a(n) = Sum_{k=1..n-1}((k mod 5)*a(n-k)), a(1) = 1.
%H Anders Hellström, <a href="/A259714/b259714.txt">Table of n, a(n) for n = 1..1000</a>
%F Conjectures from _Colin Barker_, Jul 04 2015: (Start)
%F a(n) = a(n-1)+2*a(n-2)+3*a(n-3)+4*a(n-4)+a(n-5) for n>6.
%F G.f.: x*(x-1)*(x^4+x^3+x^2+x+1) / ((x+1)*(x^4+3*x^3+2*x-1)).
%F (End)
%t 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 *)
%o (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;
%Y Cf. A088305 (sequence obtained without mod 5 in the formula).
%K nonn
%O 1,3
%A _Anders Hellström_, Jul 03 2015
|