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 1-2 of 2 results.

A271358 a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=4.

Original entry on oeis.org

4, 13, 35, 92, 241, 631, 1652, 4325, 11323, 29644, 77609, 203183, 531940, 1392637, 3645971, 9545276, 24989857, 65424295, 171283028, 448424789, 1173991339, 3073549228, 8046656345, 21066419807, 55152603076, 144391389421, 378021565187, 989673306140
Offset: 0

Views

Author

Colin Barker, Apr 05 2016

Keywords

Links

Crossrefs

Cf. A000045.
Cf. A001906 (k=0), A002878 (k=1), A100545 (k=2, without the initial 2), A271357 (k=3), this sequence (k=4), A271359 (k=5).

Programs

  • Magma
    k:=4; [k*Fibonacci(2*n+1)+(k+1)*Fibonacci(2*n): n in [0..30]]; // Bruno Berselli, Apr 06 2016
  • PARI
    a(n) = 4*fibonacci(2*n+1) + 5*fibonacci(2*n)
  • PARI
    Vec((4+x)/(1-3*x+x^2) + O(x^50))

Formula

G.f.: (4+x) / (1-3*x+x^2).
a(n) = 3*a(n-1)-a(n-2) for n>1.
a(n) = (2^(-2-n)*((11-sqrt(5))*(3+sqrt(5))^(n+1) - (11+sqrt(5))*(3-sqrt(5))^(n+1))) / sqrt(5).
a(n) = 5*Fibonacci(2*n+2) - Fibonacci(2*n+1).
a(n) = 4*A001906(n+1) + A001906(n-1).

Extensions

Changed offset and adapted definition, programs and formulas by Bruno Berselli, Apr 06 2016

A271359 a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=5.

Original entry on oeis.org

5, 16, 43, 113, 296, 775, 2029, 5312, 13907, 36409, 95320, 249551, 653333, 1710448, 4478011, 11723585, 30692744, 80354647, 210371197, 550758944, 1441905635, 3774957961, 9882968248, 25873946783, 67738872101, 177342669520, 464289136459, 1215524739857
Offset: 0

Views

Author

Colin Barker, Apr 05 2016

Keywords

Links

Crossrefs

Cf. A000045.
Cf. A001906 (k=0), A002878 (k=1), A100545 (k=2, without the initial 2), A271357 (k=3), A271358 (k=4), this sequence (k=5).

Programs

  • Magma
    k:=5; [k*Fibonacci(2*n+1)+(k+1)*Fibonacci(2*n): n in [0..30]]; // Bruno Berselli, Apr 06 2016
  • PARI
    a(n) = 5*fibonacci(2*n+1) + 6*fibonacci(2*n)
  • PARI
    Vec((5+x)/(1-3*x+x^2) + O(x^50))

Formula

G.f.: (5+x) / (1-3*x+x^2).
a(n) = 3*a(n-1)-a(n-2) for n>1.
a(n) = (2^(-2-n)*((13-sqrt(5))*(3+sqrt(5))^(n+1) - (13+sqrt(5))*(3-sqrt(5))^(n+1))) / sqrt(5).
a(n) = 6*Fibonacci(2*n+2) - Fibonacci(2*n+1) = 5*A001906(n+1) +A001906(n).

Extensions

Changed offset and adapted definition, programs and formulas by Bruno Berselli, Apr 06 2016
Showing 1-2 of 2 results.

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

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