A048697 Generalized Pellian with second term equal to 10.

1, 10, 21, 52, 125, 302, 729, 1760, 4249, 10258, 24765, 59788, 144341, 348470, 841281, 2031032, 4903345, 11837722, 28578789, 68995300, 166569389, 402134078, 970837545, 2343809168, 5658455881

Offset: 0

Author

Barry E. Williams

Keywords

• easy
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,1).

Crossrefs

Cf. A001333, A000129, A048654, A048655.

Programs

Haskell

a048697 n = a048697_list !! n
a048697_list = 1 : 10 : zipWith (+)
                        a048697_list (map (* 2) $ tail a048697_list)
-- Reinhard Zumkeller, Sep 05 2014

Maple

with(combinat): a:=n->8*fibonacci(n-1,2)+fibonacci(n,2): seq(a(n), n=1..25); # Zerinvary Lajos, Apr 04 2008

Mathematica

a[n_]:=(MatrixPower[{{1,2},{1,1}},n].{{9},{1}})[[2,1]]; Table[a[n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2,1},{1,10},35] (* Harvey P. Dale, Jul 26 2011 *)

Formula

a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=10.

a(n) = ((9+sqrt(2))(1+sqrt(2))^n - (9-sqrt(2))(1-sqrt(2))^n) / 2*sqrt(2).

G.f.: (1+8*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008