A048694 Generalized Pellian with second term equal to 7.

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

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 A309732

Adjacent sequences: A048691 A048692 A048693 * A048695 A048696 A048697

Keyword

easy,nonn

Author

Barry E. Williams

Status

approved