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A048695 Generalized Pellian with second term equal to 8. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A153873 A111325 A173056

Adjacent sequences:  A048692 A048693 A048694 * A048696 A048697 A048698

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

STATUS

approved

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Last modified June 27 21:39 EDT 2017. Contains 288804 sequences.