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A048694 Generalized Pellian with second term equal to 7. 6
1, 7, 15, 37, 89, 215, 519, 1253, 3025, 7303, 17631, 42565, 102761, 248087, 598935, 1445957, 3490849, 8427655, 20346159, 49119973, 118586105, 286292183, 691170471, 1668633125, 4028436721, 9725506567 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Pisano period lengths: 1, 1, 8, 4, 12, 8, 6, 4, 24, 12, 24, 8, 28, 6, 24, 8, 16, 24, 40, 12, ... . - R. J. Mathar, Aug 10 2012

LINKS

Table of n, a(n) for n=0..25.

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n) = ((6+sqrt(2))(1+sqrt(2))^n - (6-sqrt(2))(1-sqrt(2))^n)/2*sqrt(2).

a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=7.

G.f.: (1+5*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008

a(n) = ((1+sqrt(18))(1+sqrt(2))^n+(1-sqrt(18))(1-sqrt(2))^n)/2 offset 0. a(n) = first binomial transform of 1,6,2,12,4,24. - Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009

MAPLE

with(combinat): a:=n->5*fibonacci(n, 2)+fibonacci(n+1, 2): seq(a(n), n=0..26); # Zerinvary Lajos, Apr 04 2008

MATHEMATICA

a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{6}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)

LinearRecurrence[{2, 1}, {1, 7}, 40] (* Harvey P. Dale, Jul 22 2011 *)

PROG

(Maxima)

a[0]:1$

a[1]:7$

a[n]:=2*a[n-1]+a[n-2]$

A048694(n):=a[n]$

makelist(A048694(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */

CROSSREFS

Cf. A001333, A000129, A048654, A048655.

Sequence in context: A247606 A146837 A146044 * A041094 A042287 A145978

Adjacent sequences:  A048691 A048692 A048693 * A048695 A048696 A048697

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

STATUS

approved

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Last modified March 25 05:37 EDT 2017. Contains 284036 sequences.