A138110 - OEIS

%I #5 Mar 30 2012 18:51:57

%S 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,

%T 3,5,-5,-8,0,8,0,-13,-8,8,13,-13,-21,0,21,13,-34,-21,21,34,0,-55,0,55,

%U 34,-34,-55,55,89,0,-89,0,144,89,-89,-144,144,233,0,-233,-144,377,233,-233,-377,0,610,0,-610,-377,377

%N 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 Ignoring signs, the sequence contains A000045(2)=1 ten times and each of the following Fibonacci numbers A000045(i>2) four times.

%F T(0,n)=A138112(n). T(d,n)= T(d-1,n+1)-T(d-1,n), d=1..4.

%F T(1,n)=A100334(n-1). T(2,n)=A103311(n). T(3,n) = -A138003(n-2). T(4,n)= -A105371(n).

%F sum_(d=0..4) T(d,n)=0 (columns sum to zero).

%e All 5 rows of the table T(d,n) are:

%e .0,.0,.0,.1,.3,.5,.5,..0,-13,-34,-55,-55,...0,.144,...

%e .0,.0,.1,.2,.2,.0,-5,-13,-21,-21,..0,.55,.144,.233,...

%e .0,.1,.1,.0,-2,-5,-8,.-8,..0,.21,.55,.89,..89,...0,...

%e .1,.0,-1,-2,-3,-3,.0,..8,.21,.34,.34,..0,.-89,-233,...

%e -1,-1,-1,-1,.0,.3,.8,.13,.13,..0,-34,-89,-144,-144,...

%Y Cf. A102312 (A049666), A099100, A134489, A134490, A134491.

%K sign,tabf,less

%O 0,17

%A _Paul Curtz_, May 04 2008

%E Edited by _R. J. Mathar_, Jul 04 2008