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

Author

Paul Barry, Jul 20 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000975, A004526, A005578, A008619.

Programs

Magma

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

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 *)

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]