cp's OEIS Frontend

A283959 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 = 5.

%I A283959 #21 Nov 06 2020 03:55:26
%S A283959 1,1,1,1,1,5,13,33,85,561,1597,4229,11089,73393,209089,553873,1452529,
%T A283959 9613829,27388957,72553041,190270165,1259338113,3587744173,9503894405,
%U A283959 24923939041,164963678881,469967097601,1244937613921,3264845744161,21608982595205
%N A283959 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 = 5.
%H A283959 Seiichi Manyama, <a href="/A283959/b283959.txt">Table of n, a(n) for n = 1..1894</a>
%H A283959 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,132,0,0,0,-132,0,0,0,1).
%F A283959 a(4*k-1) = 3*a(4*k-2) - a(4*k-3) - 1,
%F A283959 a(4*k)   = 3*a(4*k-1) - a(4*k-2) - 1,
%F A283959 a(4*k+1) = 3*a(4*k)   - a(4*k-1) - 1,
%F A283959 a(4*k+2) = 7*a(4*k+1) - a(4*k)   - 1.
%F A283959 From _Colin Barker_, Nov 03 2020: (Start)
%F A283959 G.f.: x*(1 + x + x^2 + x^3 - 131*x^4 - 127*x^5 - 119*x^6 - 99*x^7 + 85*x^8 + 33*x^9 + 13*x^10 + 5*x^11) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - 131*x^4 + x^8)).
%F A283959 a(n) = 132*a(n-4) - 132*a(n-8) + a(n-12) for n>12.
%F A283959 (End)
%t A283959 a[n_]:= If[n<6, 1, (Sum[a[n-j] , {j, 4}] +  a[n - 1] a[n - 4])/a[n - 5]]; Table[a[n], {n, 30}] (* _Indranil Ghosh_, Mar 18 2017 *)
%o A283959 (PARI) a(n) = if(n<6, 1, (sum(j=1, 4, a(n - j)) + a(n - 1)*a(n - 4))/a(n - 5));
%o A283959 for(n=1, 30, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 18 2017
%Y A283959 Cf. A283330.
%Y A283959 Cf. A072881 (h=3), A283958 (h=4), this sequence (h=5), A283960 (h=6).
%K A283959 nonn
%O A283959 1,6
%A A283959 _Seiichi Manyama_, Mar 18 2017