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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A131040 a(n) = (1/2+1/2*i*sqrt(11))^n + (1/2-1/2*i*sqrt(11))^n, where i=sqrt(-1).

Original entry on oeis.org

1, -5, -8, 7, 31, 10, -83, -113, 136, 475, 67, -1358, -1559, 2515, 7192, -353, -21929, -20870, 44917, 107527, -27224, -349805, -268133, 781282, 1585681, -758165, -5515208, -3240713, 13304911, 23027050, -16887683, -85968833, -35305784
Offset: 0

Views

Author

Creighton Dement, Jun 11 2007

Keywords

Comments

Generating floretion is 1.5i' + .5j' + .5k' + .5e whereas in A131039 it is 'i + .5i' + .5j' + .5k' + .5e
Essentially the Lucas sequence V(1,3). - Peter Bala, Jun 23 2015

Links

Crossrefs

Cf. A131039, A131041, A131042, A002316, A002531.

Programs

  • Maple
    Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[ 1.5i' + .5j' + .5k' + .5e]
  • Sage
    [lucas_number2(n,1,3) for n in range(1, 34)] # Zerinvary Lajos, May 14 2009

Formula

a(n) = a(n-1) - 3*a(n-2); G.f. (1 - 6*x)/(1 - x + 3*x^2).
a(n) = [x^n] ( (1 + x + sqrt(1 + 2*x - 11*x^2))/2 )^n. - Peter Bala, Jun 23 2015

A131041 a(n) = 2*a(n-1) - a(n-2) - a(n-4).

Original entry on oeis.org

1, 1, 1, -1, -4, -8, -13, -17, -17, -9, 12, 50, 105, 169, 221, 223, 120, -152, -645, -1361, -2197, -2881, -2920, -1598, 1921, 8321, 17641, 28559, 37556, 38232, 21267, -24257, -107337, -228649, -371228, -489550, -500535, -282871, 306021
Offset: 0

Views

Author

Creighton Dement, Jun 11 2007

Keywords

Comments

Generating floretion is .5i' + .5j' + .5k' + .5e + 'ii' (for A131039 it is 'i + .5i' + .5j' + .5k' + .5e and for A131040 it is 1.5i' + .5j' + .5k' + .5e)

Links

Crossrefs

Cf. A131039, A131040, A131042, A002316, A002531.

Programs

  • Maple
    Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[.5i' + .5j' + .5k' + .5e + 'ii']
  • Mathematica
    LinearRecurrence[{2,-1,0,-1},{1,1,1,-1},40] (* Harvey P. Dale, Oct 14 2012 *)

Formula

G.f. (1-x-2*x^3)/(1-2*x+x^2+x^4)
Showing 1-2 of 2 results.

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

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