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A163834 a(n) = (4^n + 5)/3. 4
2, 3, 7, 23, 87, 343, 1367, 5463, 21847, 87383, 349527, 1398103, 5592407, 22369623, 89478487, 357913943, 1431655767, 5726623063, 22906492247, 91625968983, 366503875927, 1466015503703, 5864062014807, 23456248059223, 93824992236887, 375299968947543 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = (4^n + 5)/3 = A135351(2*n+1) = A140966(2*n) = A153643(2*n).

a(n) = 5*a(n-1) - 4*a(n-2).

G.f.: (2-7*x)/((4*x-1)*(x-1)).

a(n+1) - a(n) = A000302(n).

E.g.f.: (1/3)*(5*exp(x) + exp(4*x)). - G. C. Greubel, Aug 05 2017

MATHEMATICA

Table[(4^n + 5)/3, {n, 0, 50}] (* G. C. Greubel, Aug 05 2017 *)

PROG

(PARI) x='x+O('x^50); concat([0], Vec((2-7*x)/((4*x-1)*(x-1)))) \\ G. C. Greubel, Aug 05 2017

CROSSREFS

Cf. A000027, A135351, A140966, A153643.

Sequence in context: A084710 A088173 A129739 * A002386 A000230 A256454

Adjacent sequences:  A163831 A163832 A163833 * A163835 A163836 A163837

KEYWORD

nonn,easy

AUTHOR

Juri-Stepan Gerasimov, Aug 05 2009

EXTENSIONS

Offset set to 0 by R. J. Mathar, Aug 06 2009

STATUS

approved

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Last modified January 19 14:53 EST 2020. Contains 331049 sequences. (Running on oeis4.)