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A131572 a(0)=0 and a(1)=1, continued such that absolute values of 2nd differences equal the original sequence. 4
0, 1, 2, 2, 4, 4, 8, 8, 16, 16, 32, 32, 64, 64, 128, 128, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 8192, 8192, 16384, 16384, 32768, 32768, 65536, 65536, 131072, 131072, 262144, 262144, 524288, 524288, 1048576, 1048576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is the main sequence of a family of sequences starting at a(0)=A and a(1)=B, continuing a(3,...)= 2B, 2B, 4B, 4B, 8B, 8B, 16B, 16B, 32B, 32B, .. such that the absolute values of the 2nd differences, abs(a(n+2)-2*a(n+1)+a(n)), equal the original sequence. Alternatively starting at a(0)=a(1)=1 gives A016116.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

FORMULA

a(n) = 2*a(n-2), n>2.

O.g.f.: x*(1+2*x)/(1-2*x^2). - R. J. Mathar, Jul 16 2008

a(n) = A016116(n) - A000007(n), that is, a(0)=0, a(n)=A016116(n) for n>=1 - Bruno Berselli, Apr 13 2011

First differences: a(n+1)-a(n)=A131575(n).

Second differences: A131575(n+1)-A131575(n)= (-1)^n*a(n).

PROG

(MAGMA) [2^Floor(n/2)-0^n: n in [0..50]]; // Vincenzo Librandi, Aug 18 2011

CROSSREFS

Sequence in context: A158780 A117575 * A152166 A016116 A060546 A163403

Adjacent sequences:  A131569 A131570 A131571 * A131573 A131574 A131575

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Aug 28 2007

EXTENSIONS

Edited by R. J. Mathar, Jul 16 2008

More terms from Vincenzo Librandi, Aug 18 2011

STATUS

approved

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Last modified May 25 21:22 EDT 2017. Contains 287059 sequences.