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A153643 Jacobsthal numbers A001045 incremented by 2. 6
2, 3, 3, 5, 7, 13, 23, 45, 87, 173, 343, 685, 1367, 2733, 5463, 10925, 21847, 43693, 87383, 174765, 349527, 699053, 1398103, 2796205, 5592407, 11184813, 22369623, 44739245, 89478487, 178956973, 357913943, 715827885, 1431655767, 2863311533, 5726623063 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

FORMULA

a(n) = 2 + A001045(n) = A001045(n) + A007395(n) = 1 + A128209(n).

a(n) - A010684(n) = A078008(n), first differences of A001045. - Paul Curtz, Jan 17 2009

G.f.: (2 - x - 5*x^2)/((1+x)*(1-x)*(1-2*x)). - R. J. Mathar, Jan 23 2009

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n >= 3. - Andrew Howroyd, Feb 26 2018

MATHEMATICA

LinearRecurrence[{1, 2}, {0, 1}, 40] + 2 (* Harvey P. Dale, May 26 2014 *)

LinearRecurrence[{2, 1, -2}, {2, 3, 3}, 40] (* Georg Fischer, Apr 02 2019 *)

PROG

(PARI) my(x='x+O('x^40)); Vec( (2-x-5*x^2)/((1-x^2)*(1-2*x)) ) \\ G. C. Greubel, Apr 02 2019

(MAGMA) I:=[2, 3, 3]; [n le 3 select I[n] else 2*Self(n-1) +Self(n-2) -2*Self(n-3): n in [1..40]]; // G. C. Greubel, Apr 02 2019

(Sage) ((2-x-5*x^2)/((1-x^2)*(1-2*x))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 02 2019

(GAP) a:=[2, 3, 3];; for n in [4..40] do a[n]:=2*a[n-1]+a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Apr 02 2019

CROSSREFS

Cf. A001045, A007395, A010684, A078008, A128209.

Sequence in context: A258967 A290000 A035068 * A053218 A198335 A296335

Adjacent sequences:  A153640 A153641 A153642 * A153644 A153645 A153646

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Dec 30 2008

EXTENSIONS

Edited and extended by R. J. Mathar, Jan 23 2009

STATUS

approved

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Last modified October 21 04:26 EDT 2019. Contains 328291 sequences. (Running on oeis4.)