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A084215 G.f.: (1+x^2)/(1-2x). 8
1, 2, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720, 2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 335544320, 671088640, 1342177280, 2684354560, 5368709120, 10737418240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Associated with a math magic problem.

Elements are the sums of consecutive pairs of elements of A084214.

LINKS

Table of n, a(n) for n=0..33.

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

a(n) is the sum of top row terms of M^n, M = 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,...

... - Gary W. Adamson, Aug 26 2011

a(n) = floor(2^(n-2)*5). (* From 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

EXAMPLE

a(4) = 20 = (8 + 8 + 4) since the top row of M^4 = (8, 8, 4, 0, 0, 0,...).

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}] (* From Taher Jamshidi, Sep 15 2012 *)

CROSSREFS

Cf. A060816.

Sequence in context: A068034 A222082 A284904 * A024810 A049938 A002460

Adjacent sequences:  A084212 A084213 A084214 * A084216 A084217 A084218

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 19 2003

STATUS

approved

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Last modified May 28 16:24 EDT 2017. Contains 287241 sequences.