A283958 - OEIS

%I #17 Mar 20 2017 10:23:10

%S 1,1,1,1,4,10,25,139,391,1033,5806,16384,43345,243685,687709,1819441,

%T 10228936,28867366,76373161,429371599,1211741635,3205853305,

%U 18023378194,50864281276,134569465633,756552512521,2135088071929,5648711703265,31757182147660

%N 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.

%H Seiichi Manyama, <a href="/A283958/b283958.txt">Table of n, a(n) for n = 1..1852</a>

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

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

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

%F 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

%t 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 *)

%o (PARI) a(n) = if(n<5, 1, (sum(j=1, 3, a(n - j)) + a(n - 1)*a(n - 3))/a(n - 4));

%o for(n=1, 29, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 18 2017

%Y Cf. A283329.

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

%K nonn,easy

%O 1,5

%A _Seiichi Manyama_, Mar 18 2017