A086445 Partial sums of A005578.

1, 2, 4, 7, 13, 24, 46, 89, 175, 346, 688, 1371, 2737, 5468, 10930, 21853, 43699, 87390, 174772, 349535, 699061, 1398112, 2796214, 5592417, 11184823, 22369634, 44739256, 89478499, 178956985, 357913956, 715827898, 1431655781, 2863311547

Offset

0,2

Comments

With [0,0,0] prepended to it, this is an autosequence of the first kind. - Jean-François Alcover, Oct 21 2019

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

OEIS Wiki, Autosequence

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

Formula

G.f.: (1-x-x^2)/((1+x)(1-x)^2(1-2x)).

a(n) = 2*2^n/3+(-1)^n/12+n/2+1/4.

a(n) = A000975(n) + A008619(n).

a(0) = 1, a(n) = floor(2*a(n-1) - n/2 + 1) for n>0. - Gerald McGarvey, Aug 31 2004

a(n+1) - 2*a(n) = -floor(n/2) = -A004526(n). - Jean-François Alcover, Oct 21 2019 [noticed by Paul Curtz in a private e-mail]

Maple

A086445:=n->2*2^n/3+(-1)^n/12+n/2+1/4: seq(A086445(n), n=0..40); # Wesley Ivan Hurt, Apr 24 2017

Mathematica

CoefficientList[Series[(1-x-x^2)/((1+x)(1-x)^2(1-2x)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 05 2012 *)
LinearRecurrence[{3, -1, -3, 2}, {1, 2, 4, 7}, 40] (* Harvey P. Dale, May 28 2015 *)

Prog

(Magma) [2*2^n/3+(-1)^n/12+n/2+1/4: n in [0..40]]; // Vincenzo Librandi, Apr 05 2012

Crossrefs

Cf. A000975, A004526, A005578, A008619.

Sequence in context: A018185 A191526 A005255 * A127602 A113291 A102112

Adjacent sequences: A086442 A086443 A086444 * A086446 A086447 A086448

Keyword

nonn,easy

Author

Paul Barry, Jul 20 2003

Status

approved