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 A131572 a(0)=0 and a(1)=1, continued such that absolute values of 2nd differences equal the original sequence. 23
 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 Index entries for linear recurrences with constant coefficients, signature (0,2). 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). MATHEMATICA LinearRecurrence[{0, 2}, {0, 1, 2}, 50] (* Harvey P. Dale, Jul 10 2018 *) PROG (Magma) [2^Floor(n/2)-0^n: n in [0..50]]; // Vincenzo Librandi, Aug 18 2011 CROSSREFS The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283. - N. J. A. Sloane, Jul 14 2022 Sequence in context: A076939 A158780 A117575 * A152166 A320770 A016116 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 September 27 15:39 EDT 2022. Contains 357062 sequences. (Running on oeis4.)