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A048693 Generalized Pellian with 2nd term equal to 6. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A192304 A147330 A042607 * A041068 A037243 A107710

Adjacent sequences:  A048690 A048691 A048692 * A048694 A048695 A048696

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

STATUS

approved

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Last modified November 17 19:35 EST 2017. Contains 294834 sequences.