A375804 a(n) = Lucas(n-1) * Lucas(n+1) * Fibonacci(2*n-1) * Fibonacci(2*n+1).
12, 40, 1365, 19448, 381276, 6615103, 120241980, 2147070680, 38600066517, 692153278024, 12423591148332, 222908960952575, 4000098954110700, 71777766990248968, 1288007282149222101, 23112301389881302808, 414733773612913239420, 7442093184423393874495, 133542960264663589170972
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..798
- Hideyuki Ohtskua, proposer, Problem H-944, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 62, No. 3 (2024), p. 266.
- Index entries for linear recurrences with constant coefficients, signature (13,104,-260,-260,104,13,-1).
Programs
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Mathematica
a[n_] := LucasL[n-1] * LucasL[n+1] * Fibonacci[2*n-1] * Fibonacci[2*n+1]; Array[a, 20]
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PARI
lucas(n) = fibonacci(n-1) + fibonacci(n+1); a(n) = lucas(n-1) * lucas(n+1) * fibonacci(2*n-1) * fibonacci(2*n+1);
Formula
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(5) - 2)/ 4 = A204188 - 1/2 (Ohtskua, 2024).
G.f.: -x^2*(-20+65*x+195*x^2-84*x^3-13*x^4+x^5)/ ( (1+x) *(x^2-3*x+1) *(x^2+7*x+1) *(x^2-18*x+1) ). - R. J. Mathar, Aug 30 2024