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.

Showing 1-3 of 3 results.

A380083 a(n) = Pell(n^2)/Pell(n).

Original entry on oeis.org

1, 6, 197, 39236, 45232349, 304285766994, 11928254138546089, 2725453049877127789064, 3629520789795568149638626009, 28171611459441395148628640333550174, 1274457582507820938168220698796661580252461, 336039604487720392926819615640785342048933644491212
Offset: 1

Views

Author

Seiichi Manyama, May 08 2025

Keywords

Crossrefs

Main diagonal of A383742.

Programs

  • Maple
    a:= n-> (f->f(n^2)/f(n))(k->(<<2|1>, <1|0>>^k)[1, 2]):
    seq(a(n), n=1..12);  # Alois P. Heinz, May 08 2025
  • Mathematica
    a[n_] := Fibonacci[n^2, 2]/Fibonacci[n, 2]; Array[a, 12] (* Amiram Eldar, May 08 2025 *)
  • PARI
    pell(n) = ([2, 1; 1, 0]^n)[2, 1];
    a(n) = pell(n^2)/pell(n);

Formula

a(n) = A204327(n)/A000129(n).
a(n) = [x^n] x/(1 - A002203(n)*x + (-1)^n*x^2).

A383740 a(0) = 4; a(n) = Pell(4*n)/Pell(n) for n > 0.

Original entry on oeis.org

4, 12, 204, 2772, 39236, 551532, 7761996, 109216308, 1536797956, 21624369228, 304278011724, 4281516425748, 60245508232004, 847718631046572, 11928306344398284, 167844007448966772, 2361744410638758916, 33232265756370284172, 467613464999874177996, 6579820775754484587348
Offset: 0

Views

Author

Seiichi Manyama, May 07 2025

Keywords

Crossrefs

Row n=4 of A383742.

Programs

  • Mathematica
    a[n_] := Fibonacci[4*n, 2]/Fibonacci[n, 2]; a[0] = 4; Array[a, 20, 0] (* Amiram Eldar, May 08 2025 *)
  • PARI
    my(N=30, x='x+O('x^N)); Vec(4*(1-9*x-15*x^2+3*x^3)/((1+2*x-x^2)*(1-14*x-x^2)))

Formula

a(n) = 12*a(n-1) + 30*a(n-2) - 12*a(n-3) - a(n-4).
G.f.: 4 * (1-9*x-15*x^2+3*x^3)/((1+2*x-x^2) * (1-14*x-x^2)).

A383741 a(0) = 5; a(n) = Pell(5*n)/Pell(n) for n > 0.

Original entry on oeis.org

5, 29, 1189, 39005, 1332869, 45232349, 1536836005, 52205623709, 1773463509509, 60245500431005, 2046573861616549, 69523263984968669, 2361744412174224005, 80229786688466775389, 2725451003353980465829, 92585104325258634975005, 3145168096067610728884229
Offset: 0

Views

Author

Seiichi Manyama, May 07 2025

Keywords

Crossrefs

Row n=5 of A383742.

Programs

  • Mathematica
    a[n_] := Fibonacci[5*n, 2]/Fibonacci[n, 2]; a[0] = 5; Array[a, 17, 0] (* Amiram Eldar, May 08 2025 *)
  • PARI
    my(N=30, x='x+O('x^N)); Vec((5-116*x-522*x^2+348*x^3+29*x^4)/((1-x)*(1+6*x+x^2)*(1-34*x+x^2)))

Formula

a(n) = 29*a(n-1) + 174*a(n-2) - 174*a(n-3) - 29*a(n-4) + a(n-5).
G.f.: (5-116*x-522*x^2+348*x^3+29*x^4)/((1-x) * (1+6*x+x^2) * (1-34*x+x^2)).
Showing 1-3 of 3 results.