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A087452 G.f.: (2-x)/((1+3x)(1-4x)); e.g.f.: exp(4x)+exp(-3x); a(n)=4^n+(-3)^n. 1
2, 1, 25, 37, 337, 781, 4825, 14197, 72097, 242461, 1107625, 4017157, 17308657, 65514541, 273218425, 1059392917, 4338014017, 17050729021, 69106897225, 273715645477, 1102998412177, 4387586157901, 17623567104025, 70274600998837, 281757406247137 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Generalized Lucas-Jacobsthal numbers.

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (1,12).

FORMULA

The sequence 1, 25, 37, ... is 4*4^n-3*(-3)^n.

a(0)=2, a(1)=1, a(n)=a(n-1)+12*a(n-2) for n>1. [From Philippe Deléham, Sep 19 2009]

a(n) = 2*A053404(n) - A053404(n-1), n>0. - Ralf Stephan, Jul 21 2013

MATHEMATICA

CoefficientList[Series[(2 - z)/((1 + 3 z) (1 - 4 z)), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)

PROG

(PARI) polsym(x^2-x-12, 50) \\ Charles R Greathouse IV, Jun 11 2011

CROSSREFS

Cf. A014551, A087451.

Sequence in context: A013313 A013317 A010256 * A098878 A235031 A138955

Adjacent sequences:  A087449 A087450 A087451 * A087453 A087454 A087455

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 06 2003

STATUS

approved

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Last modified December 7 23:55 EST 2016. Contains 278902 sequences.