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.
1, 1, 1, 1, 1, 5, 13, 33, 85, 561, 1597, 4229, 11089, 73393, 209089, 553873, 1452529, 9613829, 27388957, 72553041, 190270165, 1259338113, 3587744173, 9503894405, 24923939041, 164963678881, 469967097601, 1244937613921, 3264845744161, 21608982595205
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..1894
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,132,0,0,0,-132,0,0,0,1).
Programs
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Mathematica
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 *) -
PARI
a(n) = if(n<6, 1, (sum(j=1, 4, a(n - j)) + a(n - 1)*a(n - 4))/a(n - 5)); for(n=1, 30, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 18 2017
Formula
a(4*k-1) = 3*a(4*k-2) - a(4*k-3) - 1,
a(4*k) = 3*a(4*k-1) - a(4*k-2) - 1,
a(4*k+1) = 3*a(4*k) - a(4*k-1) - 1,
a(4*k+2) = 7*a(4*k+1) - a(4*k) - 1.
From Colin Barker, Nov 03 2020: (Start)
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)).
a(n) = 132*a(n-4) - 132*a(n-8) + a(n-12) for n>12.
(End)
Comments