A110906 Expansion of (1 +34*x +121*x^2)/((1-x)*(x^2 -14*x +1)).

1, 49, 841, 11881, 165649, 2307361, 32137561, 447618649, 6234523681, 86835713041, 1209465459049, 16845680713801, 234630064534321, 3267975222766849, 45517023054201721, 633970347536057401

Offset

0,2

Comments

A floretion-generated sequence of squares.

Floretion Algebra Multiplication Program, FAMP Code: 1vescycseq[C*B] with C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' B = - 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj'

Links

G. C. Greubel, Table of n, a(n) for n = 0..870

Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

Formula

a(n) = -13 + 14*A007655(n+2) - 134*A007655(n+1). - R. J. Mathar, Nov 10 2009

From Colin Barker, May 06 2019: (Start)

a(n) = -13 + (7-4*sqrt(3))^n*(7+(3*sqrt(3))/2) + (7-(3*sqrt(3))/2)*(7+4*sqrt(3))^n.

a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3) for n>2. (End)

Mathematica

CoefficientList[Series[(1 + 34*x + 121*x^2)/((1 - x)*(x^2 - 14*x + 1)), {x, 0, 50}], x] (* G. C. Greubel, Oct 19 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1 +34*x +121*x^2)/((1-x)*(x^2 -14*x +1))) \\ G. C. Greubel, Oct 19 2017

Crossrefs

Sequence in context: A289992 A357653 A278284 * A193940 A012115 A284642

Adjacent sequences: A110903 A110904 A110905 * A110907 A110908 A110909

Keyword

easy,nonn

Author

Creighton Dement, Sep 21 2005

Status

approved