A153643 Jacobsthal numbers A001045 incremented by 2.

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

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: A035066 A258967 A035068 * A053218 A198335 A339050

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