cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

0, 20, 195, 4420, 72624, 1347905, 23877840, 430583140, 7712000835, 138485573876, 2484341814240, 44584372180225, 800002107309600, 14355674602647860, 257600625681170499, 4622465972012379940, 82946715695078486160, 1488418904383171787585, 26708590219470770907120
Offset: 1

Views

Author

Amiram Eldar, Aug 29 2024

Keywords

Links

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

A375804 a(n) = Lucas(n-1) * Lucas(n+1) * Fibonacci(2*n-1) * Fibonacci(2*n+1).

Original entry on oeis.org

12, 40, 1365, 19448, 381276, 6615103, 120241980, 2147070680, 38600066517, 692153278024, 12423591148332, 222908960952575, 4000098954110700, 71777766990248968, 1288007282149222101, 23112301389881302808, 414733773612913239420, 7442093184423393874495, 133542960264663589170972
Offset: 1

Views

Author

Amiram Eldar, Aug 29 2024

Keywords

Links

Crossrefs

Cf. A000032, A000045, A064170, A204188, A292696, A375803.

Programs

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

a(n) = A292696(n) * A064170(n+2).
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
Previous Showing 11-12 of 12 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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