Search: id:A112455
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%I A112455
%S A112455 3,0,2,3,2,5,1,7,6,6,13,0,19,13,19,32,6,51,26,57,77,31,134,46,165,180,
%T A112455 119,345,61,464,406,403,870,3,1273,873,1270,2146,397,3416,1749,3813,
%U A112455 5165,2064,8978,3101,11042,12079,7941,23121,4138,31062,27259,26924
%V A112455 -3,0,2,3,-2,-5,-1,7,6,-6,-13,0,19,13,-19,-32,6,51,26,-57,-77,31,134,46,
               -165,-180,119,
%W A112455 345,61,-464,-406,403,870,3,-1273,-873,1270,2146,-397,-3416,-1749,3813,
               5165,-2064,
%X A112455 -8978,-3101,11042,12079,-7941
%N A112455 a(n) = -a(n-2)-a(n-3).
%C A112455 This sequence resembles the Perrin sequence, A001608. Like many such 
               sequences with a(1)=0, any prime p divides a(p). The first pseudoprime 
               (composite n divides a(n)) is 121.
%F A112455 a(n)= - trace({{0, 0, -1}, {1, 0, -1}, {0, 1, 0}})^n - Artur Jasinski 
               (grafix(AT)csl.pl), Jan 10 2007
%F A112455 G.f.: -(3+x^2)/(1+x^2+x^3). a(n) = -3*A077962(n)-A077962(n-2). [From 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2009]
%p A112455 Table[ -Tr[MatrixPower[{{0, 0, -1}, {1, 0, -1}, {0, 1, 0}}, n]], {n, 
               1, 50}] - Artur Jasinski (grafix(AT)csl.pl), Jan 10 2007
%Y A112455 Cf. A001608, A112458.
%Y A112455 Sequence in context: A119493 A032531 A143394 this_sequence A001608 A159977 
               A112974
%Y A112455 Adjacent sequences: A112452 A112453 A112454 this_sequence A112456 A112457 
               A112458
%K A112455 sign
%O A112455 0,1
%A A112455 Anthony C Robin (anthony_robin(AT)hotmail.com), Dec 13 2005
%E A112455 Edited by Don Reble (djr(AT)nk.ca), Jan 25 2006

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