A283958 a(n) = (Sum_{j=1..h-1} a(n-j) + a(n-1)*a(n-h+1))/a(n-h) with a(1), ..., a(h)=1, where h = 4.

1, 1, 1, 1, 4, 10, 25, 139, 391, 1033, 5806, 16384, 43345, 243685, 687709, 1819441, 10228936, 28867366, 76373161, 429371599, 1211741635, 3205853305, 18023378194, 50864281276, 134569465633, 756552512521, 2135088071929, 5648711703265, 31757182147660

Offset: 1

Author

Seiichi Manyama, Mar 18 2017

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1852

Crossrefs

Cf. A283329.

Cf. A072881 (h=3), this sequence (h=4), A283959 (h=5), A283960 (h=6).

Programs

Mathematica

a[n_]:= If[n<5, 1, (Sum[a[n-j] , {j, 3}] +  a[n - 1] a[n - 3])/a[n - 4]]; Table[a[n], {n, 29}] (* Indranil Ghosh, Mar 18 2017 *)

PARI

a(n) = if(n<5, 1, (sum(j=1, 3, a(n - j)) + a(n - 1)*a(n - 3))/a(n - 4));
for(n=1, 29, print1(a(n),", ")) \\ Indranil Ghosh, Mar 18 2017

Formula

a(3*k) = 3*a(3*k-1) - a(3*k-2) - 1,

a(3*k+1) = 3*a(3*k) - a(3*k-1) - 1,

a(3*k+2) = 6*a(3*k+1) - a(3*k) - 1.

G.f.: -x*(4*x^8 + 10*x^7 + 25*x^6 - 33*x^5 - 39*x^4 - 42*x^3 + x^2 + x + 1) / ((x - 1)*(x^2 + x + 1)*(x^6 - 42*x^3 + 1)). - Alois P. Heinz, Mar 20 2017