Search: id:A138110
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%I A138110
%S A138110 0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,1,2,0,2,1,3,2,2,3,0,5,0,5,3,3,5,5,8,0,8,
%T A138110 0,13,8,8,13,13,21,0,21,13,34,21,21,34,0,55,0,55,34,34,55,55,89,0,89,0,
%U A138110 144,89,89,144,144,233,0,233,144,377,233,233,377,0,610,0,610,377,377
%V A138110 0,0,0,1,-1,0,0,1,0,-1,0,1,1,-1,-1,1,2,0,-2,-1,3,2,-2,-3,0,5,0,-5,-3,3,
               5,-5,-8,0,8,0,
%W A138110 -13,-8,8,13,-13,-21,0,21,13,-34,-21,21,34,0,-55,0,55,34,-34,-55,55,89,
               0,-89,0,144,89,
%X A138110 -89,-144,144,233,0,-233,-144,377,233,-233,-377,0,610,0,-610,-377,377
%N A138110 Table T(d,n) read column by column: the n-th term in the sequence of 
               the d-th differences of A138112, d=0..4.
%C A138110 Ignoring signs, the sequence contains A000045(2)=1 ten times and each 
               of the following Fibonacci numbers A000045(i>2) four times.
%F A138110 T(0,n)=A138112(n). T(d,n)= T(d-1,n+1)-T(d-1,n), d=1..4.
%F A138110 T(1,n)=A100334(n-1). T(2,n)=A103311(n). T(3,n) = -A138003(n-2). T(4,n)= 
               -A105371(n).
%F A138110 sum_(d=0..4) T(d,n)=0 (columns sum to zero).
%e A138110 All 5 rows of the table T(d,n) are:
%e A138110 .0,.0,.0,.1,.3,.5,.5,..0,-13,-34,-55,-55,...0,.144,...
%e A138110 .0,.0,.1,.2,.2,.0,-5,-13,-21,-21,..0,.55,.144,.233,...
%e A138110 .0,.1,.1,.0,-2,-5,-8,.-8,..0,.21,.55,.89,..89,...0,...
%e A138110 .1,.0,-1,-2,-3,-3,.0,..8,.21,.34,.34,..0,.-89,-233,...
%e A138110 -1,-1,-1,-1,.0,.3,.8,.13,.13,..0,-34,-89,-144,-144,...
%Y A138110 Cf. A102312 (A049666), A099100, A134489, A134490, A134491.
%Y A138110 Sequence in context: A029184 A029221 A029183 this_sequence A080233 A156644 
               A097808
%Y A138110 Adjacent sequences: A138107 A138108 A138109 this_sequence A138111 A138112 
               A138113
%K A138110 sign,tabf,less
%O A138110 0,17
%A A138110 Paul Curtz (bpcrtz(AT)free.fr), May 04 2008
%E A138110 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 04 2008

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