A048879 Generalized Pellian with second term of 10.

1, 10, 41, 174, 737, 3122, 13225, 56022, 237313, 1005274, 4258409, 18038910, 76414049, 323695106, 1371194473, 5808472998, 24605086465, 104228818858, 441520361897, 1870310266446, 7922761427681, 33561355977170, 142168185336361, 602234097322614

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 (4,1)

Formula

a(n) = ((8+sqrt(5))*(2+sqrt(5))^n - (8-sqrt(5))*(2-sqrt(5))^n)2*sqrt(5).

From Philippe Deléham, Nov 03 2008: (Start)

a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=10.

G.f.: (1+6*x)/(1-4*x-x^2). (End)

For n >= 1, a(n) equals the denominator of the continued fraction [4, 4, ..., 4, 10] (with n copies of 4). The numerator of that continued fraction is a(n+1). - ZhenShu Luan, Aug 05 2019

Maple

with(combinat): a:=n->6*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008

Mathematica

LinearRecurrence[{4, 1}, {1, 10}, 30] (* Harvey P. Dale, Jul 18 2011 *)

Prog

(Haskell)
a048879 n = a048879_list !! n
a048879_list = 1 : 10 : zipWith (+)
                        a048879_list (map (* 4) $ tail a048879_list)
-- Reinhard Zumkeller, Mar 03 2014

Crossrefs

Cf. A015448, A001077, A001076, A033887.

Sequence in context: A294604 A061003 A211064 * A221805 A089211 A220927

Adjacent sequences: A048876 A048877 A048878 * A048880 A048881 A048882

Keyword

easy,nice,nonn

Author

Barry E. Williams

Extensions

More terms from Harvey P. Dale, Jul 18 2011

Status

approved