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.

A092164 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,1) entry of M^n.

Original entry on oeis.org

1, 11, 61, 371, 2221, 13331, 79981, 479891, 2879341, 17276051, 103656301, 621937811, 3731626861, 22389761171, 134338567021, 806031402131, 4836188412781, 29017130476691, 174102782860141, 1044616697160851
Offset: 1

Views

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004

Keywords

Crossrefs

Programs

  • Mathematica
    Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[1, 1]], {n, 20}] (* Robert G. Wilson v, Apr 22 2004 *)

Formula

a(n) = (2*6^n + 5*(-1)^n)/7.
A092165 +(-1)^n.
a(n)=5*a(n-1)+6*a(n-2). G.f.: x*(1+6*x)/((1+x)*(1-6*x)). - R. J. Mathar, Apr 20 2009

Extensions

Edited by Robert G. Wilson v, Apr 22 2004

A092165 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,2) entry of M^n.

Original entry on oeis.org

2, 10, 62, 370, 2222, 13330, 79982, 479890, 2879342, 17276050, 103656302, 621937810, 3731626862, 22389761170, 134338567022, 806031402130, 4836188412782, 29017130476690, 174102782860142, 1044616697160850, 6267700182965102, 37606201097790610, 225637206586743662
Offset: 1

Views

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004

Keywords

Crossrefs

Programs

  • Magma
    [(2*6^n - 2*(-1)^n)/7: n in [1..30]]; // Vincenzo Librandi, Jul 21 2015
  • Mathematica
    Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[1, 2]], {n, 20}] (* Robert G. Wilson v, Apr 22 2004 *)
    LinearRecurrence[{5, 6}, {2, 10}, 25] (* Vincenzo Librandi, Jul 21 2015 *)

Formula

a(n) = (2*6^n - 2*(-1)^n)/7.
a(n) = A092164(n) -(-1)^n.
From R. J. Mathar, Apr 20 2009: (Start)
a(n) = 5*a(n-1) + 6*a(n-2) = 2*A015540(n).
G.f.: 2*x/((1+x)*(1-6*x)). (End)

Extensions

Edited by Robert G. Wilson v, Apr 22 2004
More terms from Vincenzo Librandi, Jul 21 2015

A092166 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,1) entry of M^n.

Original entry on oeis.org

5, 25, 155, 925, 5555, 33325, 199955, 1199725, 7198355, 43190125, 259140755, 1554844525, 9329067155, 55974402925, 335846417555, 2015078505325, 12090471031955, 72542826191725, 435256957150355, 2611541742902125
Offset: 1

Views

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004

Keywords

Crossrefs

Programs

  • Mathematica
    Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[2, 1]], {n, 20}] (* Robert G. Wilson v, Apr 22 2004 *)

Formula

a(n) = (5*6^n - 5*(-1)^n)/7.
a(n) = A092167(n) +(-1)^n.
From Colin Barker, Nov 08 2012: (Start)
a(n) = 5*a(n-1) + 6*a(n-2).
G.f.: -5*x/((x+1)*(6*x-1)). (End)

Extensions

Edited by Robert G. Wilson v, Apr 22 2004
Showing 1-3 of 3 results.