A105082 Expansion of (5+4x)/(1-2x-x^2).

5, 14, 33, 80, 193, 466, 1125, 2716, 6557, 15830, 38217, 92264, 222745, 537754, 1298253, 3134260, 7566773, 18267806, 44102385, 106472576, 257047537, 620567650, 1498182837, 3616933324, 8732049485, 21081032294, 50894114073

Offset

0,1

Comments

A floretion-generated, Pellian related sequence.

Floretion Algebra Multiplication Program, FAMP Code: lesloop(infty)-tesforseq[ + .25'i + .25i' - .25'ii' - .25'jj' - .25'kk' + .25'jk' + .25'kj' - .25e ], Fortype: 1A.

For n > 0: A048696(n) = a(n) - a(n-1). - Reinhard Zumkeller, Dec 15 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

A. F. Horadam, Pell Identities, Fib. Quart., Vol. 9, No. 3, 1971, pp. 245-252.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (2,1).

Formula

a(n+2) = 2*a(n+1) + a(n); FAMP result: a(n) = 2*A001333(n) + 3*A048654(n); SuperSeeker results: a(n+1) - a(n) = A048696(n+1); a(n) + a(n+1) = A048696(n+2)

a(n) = ((9+5*sqrt(2))*(1+sqrt(2))^n - (9-5*sqrt(2))*(1-sqrt(2))^n)/(2*sqrt(2)) - Lambert Herrgesell (zero815(AT)googlemail.com), Jan 26 2007

Prog

(Haskell)
a105082 n = a105082_list !! n
a105082_list = scanl (+) 5 $ tail a048696_list
-- Reinhard Zumkeller, Dec 15 2013

Crossrefs

Cf. A001333, A048654, A048696.

Cf. A048772.

Sequence in context: A038090 A094002 A188589 * A059821 A296010 A182738

Adjacent sequences: A105079 A105080 A105081 * A105083 A105084 A105085

Keyword

nonn,easy

Author

Creighton Dement, Apr 06 2005

Status

approved