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

Author

Barry E. Williams

Keywords

• easy
• nonn

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,1)

Crossrefs

Cf. A001333, A000129, A048654, A048655.

Programs

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 *)

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