A127979 a(n) = (5*n/18 + 19/54)*2^n - (-1)^(n-1)*(3*n + 4)/27.

1, 4, 9, 24, 55, 130, 293, 660, 1459, 3206, 6977, 15096, 32463, 69482, 148061, 314332, 665067, 1402958, 2951545, 6194368, 12971271, 27107634, 56545429, 117751204, 244823075, 508287510, 1053857713, 2182280840, 4513692479, 9325646586

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

W. Bosma, Signed bits and fast exponentiation, Journal de Théorie des Nombres de Bordeaux, Vol. 13, Fasc. 1 (2001), p. 37 (Proposition 5).

Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-4).

Formula

G.f.: x*(1+2*x-2*x^2-2*x^3)/((1+x)^2*(1-2x)^2). - Bruno Berselli, Apr 02 2012

a(n) = 2*a(n-1)+3*a(n-2)-4*a(n-3)-4*a(n-4). - Wesley Ivan Hurt, May 07 2021

Mathematica

Table[(5n/18 + 19/54)2^(n) - ((-1)^(n - 1) )(3n + 4)/27, {n, 1, 100}]
LinearRecurrence[{2, 3, -4, -4}, {1, 4, 9, 24}, 50] (* G. C. Greubel, May 08 2018 *)

Prog

(PARI) for(n=1, 50, print1((5*n/18 +19/54)*2^n -(-1)^(n-1)*(3*n+4)/27, ", ")) \\ G. C. Greubel, May 08 2018
(Magma) [(5*n/18 +19/54)*2^n -(-1)^(n-1)*(3*n+4)/27: n in [1..50]]; // G. C. Greubel, May 08 2018

Crossrefs

Cf. A073371, A127976, A127978, A073371.

Sequence in context: A056575 A056032 A304908 * A112262 A077922 A081149

Adjacent sequences: A127976 A127977 A127978 * A127980 A127981 A127982

Keyword

nonn,easy

Author

Artur Jasinski, Feb 09 2007

Status

approved