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

Cf. A092165, A092166, A092167.

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

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

Links

Crossrefs

Cf. A092164, A092165, A092167.

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

A092167 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (2,2) entry of M^n.

Original entry on oeis.org

4, 26, 154, 926, 5554, 33326, 199954, 1199726, 7198354, 43190126, 259140754, 1554844526, 9329067154, 55974402926, 335846417554, 2015078505326, 12090471031954, 72542826191726, 435256957150354, 2611541742902126
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A092164, A092165, A092166.

Programs

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

Formula

a(n) = (5*6^n + 2*(-1)^n)/7.
A092166 -(-1)^n.
From R. J. Mathar, Apr 20 2009: (Start)
a(n) = 5*a(n-1) + 6*a(n-2).
G.f.: 2*x*(2+3*x)/((1+x)*(1-6*x)). (End)

Extensions

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

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

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