A048695 Generalized Pellian with second term equal to 8.

1, 8, 17, 42, 101, 244, 589, 1422, 3433, 8288, 20009, 48306, 116621, 281548, 679717, 1640982, 3961681, 9564344, 23090369, 55745082, 134580533, 324906148, 784392829, 1893691806, 4571776441, 11037244688

Offset

0,2

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)=8.

a(n) = ((7+sqrt(2))(1+sqrt(2))^n - (7-sqrt(2))(1-sqrt(2))^n)/2*sqrt(2).

G.f.: (1+6*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008

Maple

with(combinat): a:=n->6*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].{{7}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2, 1}, {1, 8}, 30] (* Harvey P. Dale, May 01 2013 *)

Crossrefs

Cf. A001333, A000129, A048654, A048655.

Sequence in context: A188129 A041849 A041124 * A329768 A153873 A111325

Adjacent sequences: A048692 A048693 A048694 * A048696 A048697 A048698

Keyword

easy,nonn

Author

Barry E. Williams

Status

approved