A048693 Generalized Pellian with 2nd term equal to 6.

1, 6, 13, 32, 77, 186, 449, 1084, 2617, 6318, 15253, 36824, 88901, 214626, 518153, 1250932, 3020017, 7290966, 17601949, 42494864, 102591677, 247678218, 597948113, 1443574444, 3485097001, 8413768446

Offset

0,2

Comments

Pisano period lengths: 1, 2, 8, 4, 12, 8, 6, 8, 24, 12, 24, 8, 28, 6, 24, 16, 16, 24, 40, 12, ... (is this A175181?). - 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) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=6.

G.f.: (1+4*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008

a(n) = 4*A000129(n) + A000129(n+1). - R. J. Mathar, Aug 10 2012

Example

a(n)=[ (5+sqrt(2))(1+sqrt(2))^n-(5-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2)

Maple

with(combinat): a:=n->4*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); # Zerinvary Lajos, Apr 04 2008

Mathematica

a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{5}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2, 1}, {1, 6}, 30] (* Harvey P. Dale, Mar 29 2013 *)

Prog

(Maxima)
a[0]:1$
a[1]:6$
a[n]:=2*a[n-1]+a[n-2]$
A048693(n):=a[n]$
makelist(A048693(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */

Crossrefs

Cf. A001333, A000129, A048654, A048655.

Sequence in context: A343544 A147330 A042607 * A041068 A300430 A300634

Adjacent sequences: A048690 A048691 A048692 * A048694 A048695 A048696

Keyword

easy,nonn

Author

Barry E. Williams

Status

approved