OFFSET
0,2
COMMENTS
Associated with a math magic problem.
Elements are the sums of consecutive pairs of elements of A084214.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2).
FORMULA
a(n) = Sum_{k=0..n} 2^(n-k)*binomial(1, k/2)*(1+(-1)^k)/2. - Paul Barry, Oct 15 2004
a(n) = A020714(n-2), n > 1. - R. J. Mathar, Dec 19 2008
From Gary W. Adamson, Aug 26 2011: (Start)
a(n) is the sum of top row terms of M^n, M is an infinite square production matrix as follows:
1, 1, 0, 0, 0, 0, ...
1, 1, 1, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, ...
...
E.g.: a(4) = 20 = (8 + 8 + 4) since the top row of M^4 = (8, 8, 4, 0, 0, 0, ...). (End)
a(n) = floor(2^(n-2)*5). - Taher Jamshidi, Sep 15 2012
a(n) = 2*a(n-1) for n >= 3, a(0) = 1, a(1) = 2, a(2) = 5. - Philippe Deléham, Mar 13 2013
E.g.f.: (5*exp(2*x) - 2*x - 1)/4. - Stefano Spezia, Feb 20 2023
MATHEMATICA
Join[{1, 2, a = 5}, Table[a = 2*a, {n, 0, 40}]] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
Table[Int[2^(n-2)*5], {n, 0, 40}] (* Taher Jamshidi, Sep 15 2012 *)
CoefficientList[Series[(1 + x^2)/(1 - 2 x), {x, 0, 30}], x] (* G. C. Greubel, Oct 08 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1+x^2)/(1-2*x)) \\ G. C. Greubel, Oct 08 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x^2)/(1-2*x))); // G. C. Greubel, Oct 08 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 19 2003
STATUS
approved