A375803 a(n) = Fibonacci(n-1) * Fibonacci(n+1) * Fibonacci(2*n-1) * Fibonacci(2*n+1).

0, 20, 195, 4420, 72624, 1347905, 23877840, 430583140, 7712000835, 138485573876, 2484341814240, 44584372180225, 800002107309600, 14355674602647860, 257600625681170499, 4622465972012379940, 82946715695078486160, 1488418904383171787585, 26708590219470770907120

Offset: 1

Author

Amiram Eldar, Aug 29 2024

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000045, A059929, A064170, A134944, A374149, A375804.

Programs

Mathematica

a[n_] := Fibonacci[n-1] * Fibonacci[n+1] * Fibonacci[2*n-1] * Fibonacci[2*n+1]; Array[a, 20]

PARI

a(n) = fibonacci(n-1) * fibonacci(n+1) * fibonacci(2*n-1) * fibonacci(2*n+1);

Formula

a(n) = A059929(n-1) * A059929(2*n-1) = A059929(n-1) * A064170(n+2).

Sum_{n>=2} (-1)^n/a(n) = (5*sqrt(5) - 11)/4 = A374149 - 11/2 = 10 * A134944 - 4 (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^2-18*x+1)*(x^2+7*x+1) ). - R. J. Mathar, Aug 30 2024