A329421 a(n) = gcd(A330050(n), A330051(n)).
0, 3, 2, 7, 25, 72, 52, 141, 510, 1353, 979, 2576, 9320, 24447, 17690, 46347, 167685, 439128, 317756, 831985, 3010150, 7880997, 5702743, 14930208, 54018000, 141421803, 102333778, 267913919, 969321665, 2537719272, 1836310916, 4807525989, 17393792430, 45537545553
Offset: 0
Examples
G.f. = 3*x + 2*x^2 + 7*x^3 + 25*x^4 + 72*x^5 + 52*x^6 + 141*x^7 + ...
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
a[ n_] := With[{i = 1 + Quotient[n, 2], j = 1 + 2 Mod[n, 2] + 3 Quotient[n, 2]}, If[ Mod[n, 4] > 1, Fibonacci[j] - Fibonacci[i], LucasL[j] - LucasL[i]]]; -
PARI
{a(n) = my(i=n\2+1, j=n%2+i+n, F=fibonacci, L=x->F(x+1)+F(x-1), h=if(n\2%2, x->F(x), x->L(x))); h(j)-h(i)};
Formula
a(n) = -a(-2-n) for all odd n in Z. a(4*n-1) = A215042(n) for all n in Z.
Conjectures from Colin Barker, Dec 02 2019: (Start)
G.f.: x*(1 + x)*(3 - x + 8*x^2 + 17*x^3 - 8*x^4 + 18*x^5 - 24*x^6 + 9*x^7 - x^9 + 8*x^10 + 2*x^11 + x^12) / ((1 + 4*x^2 - x^4)*(1 + x^2 - x^4)*(1 - x^2 - x^4)*(1 - 4*x^2 - x^4)).
a(n) = 21*a(n-4) - 56*a(n-8) + 21*a(n-12) - a(n-16) for n>15.
(End)
Comments