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A048878 Generalized Pellian with second term of 9. 4
1, 9, 37, 157, 665, 2817, 11933, 50549, 214129, 907065, 3842389, 16276621, 68948873, 292072113, 1237237325, 5241021413, 22201322977, 94046313321, 398386576261, 1687592618365, 7148757049721, 30282620817249 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1584

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (4,1).

FORMULA

a(n) = ( (7+sqrt(5))(2+sqrt(5))^n - (7-sqrt(5))(2-sqrt(5))^n )/2*sqrt(5).

G.f.: (1+5*x)/(1-4*x-x^2). [Philippe Deléham, Nov 03 2008]

EXAMPLE

a(n) = 4a(n-1) + a(n-2); a(0)=1, a(1)=9.

MAPLE

with(combinat): a:=n->5*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008

MATHEMATICA

LinearRecurrence[{4, 1}, {1, 9}, 31] (* or *) CoefficientList[ Series[ (1+5x)/(1-4x-x^2), {x, 0, 30}], x] (* Harvey P. Dale, Jul 12 2011 *)

PROG

(PARI) { default(realprecision, 2000); for (n=0, 2000, a=round(((7+sqrt(5))*(2+sqrt(5))^n - (7-sqrt(5))*(2-sqrt(5))^n )/10*sqrt(5)); if (a > 10^(10^3 - 6), break); write("b048878.txt", n, " ", a); ); } \\ Harry J. Smith, May 31 2009

CROSSREFS

Cf. A015448, A001077, A001076, A033887.

Sequence in context: A271908 A257448 A026620 * A246315 A232250 A201441

Adjacent sequences:  A048875 A048876 A048877 * A048879 A048880 A048881

KEYWORD

easy,nice,nonn

AUTHOR

Barry E. Williams

STATUS

approved

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Last modified March 25 15:14 EDT 2017. Contains 284082 sequences.