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A086445
Partial sums of A005578.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jul 20 2003
STATUS
approved