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%I #17 Dec 05 2019 09:27:06
%S 0,3,2,7,25,72,52,141,510,1353,979,2576,9320,24447,17690,46347,167685,
%T 439128,317756,831985,3010150,7880997,5702743,14930208,54018000,
%U 141421803,102333778,267913919,969321665,2537719272,1836310916,4807525989,17393792430,45537545553
%N a(n) = gcd(A330050(n), A330051(n)).
%H Colin Barker, <a href="/A329421/b329421.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = -a(-2-n) for all odd n in Z. a(4*n-1) = A215042(n) for all n in Z.
%F Conjectures from _Colin Barker_, Dec 02 2019: (Start)
%F 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)).
%F a(n) = 21*a(n-4) - 56*a(n-8) + 21*a(n-12) - a(n-16) for n>15.
%F (End)
%e G.f. = 3*x + 2*x^2 + 7*x^3 + 25*x^4 + 72*x^5 + 52*x^6 + 141*x^7 + ...
%t 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]]];
%o (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)};
%Y Cf. A215042, A330050, A330051.
%K nonn,easy
%O 0,2
%A _Michael Somos_, Nov 30 2019
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