OFFSET
0,2
COMMENTS
Partial sums of A014551. The inverse binomial transform yields a sequence 0,2,-1,5,-7,17,...: zero followed by a sign alternating A014551.
The table of a(n) plus higher order differences in successive rows shows A131577 on the main diagonal.
a(n) = 2^n when n is odd and 2^n-1 when n is even. - Wesley Ivan Hurt, Nov 15 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).
FORMULA
G.f.: x*(2-x)/((1-x)*(1-2*x)*(1+x)).
a(n) = 2^n - (1+(-1)^n)/2.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
a(n+1) - 2*a(n) = A168361(n).
E.g.f.: exp(2*x) - cosh(x). - G. C. Greubel, May 28 2016
a(n) = Sum_{k=1..n+1} Sum_{i=0..n+1} C(n-k,i). - Wesley Ivan Hurt, Sep 22 2017
MAPLE
MATHEMATICA
LinearRecurrence[{2, 1, -2}, {0, 2, 3}, 40] (* Harvey P. Dale, Oct 16 2012 *)
PROG
(Magma) [2^n -(1+(-1)^n)/2: n in [0..30]]; // Vincenzo Librandi, May 16 2011
(Haskell)
a166920 n = a166920_list !! n
a166920_list = scanl (+) 0 a014551_list
-- Reinhard Zumkeller, Jan 02 2013
(PARI) a(n)=2^n-(1+(-1)^n)/2 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 23 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Mar 02 2010
STATUS
approved