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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A001333, A000129, A048654, A048655.

Sequence in context: A219884 A042309 A215757 * A090076 A231966 A156592

Adjacent sequences: A048694 A048695 A048696 * A048698 A048699 A048700

Keyword

easy,nonn

Author

Barry E. Williams

Status

approved