A113020 - OEIS

%I #5 Oct 25 2012 07:02:09

%S 0,0,1,0,2,-1,0,3,-3,2,0,4,-6,8,-3,0,5,-10,20,-15,5,0,6,-15,40,-45,30,

%T -8,0,7,-21,70,-105,105,-56,13,0,8,-28,112,-210,280,-224,104,-21,0,9,

%U -36,168,-378,630,-672,468,-189,34,0,10,-45,240,-630,1260,-1680,1560,-945,340,-55

%N Number triangle whose row sums are the Fibonacci numbers.

%C Row sums sequence is A000045, F(n).

%C Main diagonal is (-1)^(n+1)F(n).

%C Absolute row sums sequence is A001906, F(2n).

%C Diagonal sums are A113021.

%H Olivier Gérard, <a href="/A113020/b113020.txt">Table of n, a(n) for n = 0..230</a>

%F T(n, k)=sum{j=0..n, C(n, j)C(0, j-k)F(j-2k)}.

%e Rows begin

%e 0;

%e 0,1;

%e 0,2,-1;

%e 0,3,-3,2;

%e 0,4,-6,8,-3;

%e 0,5,-10,20,-15,5;

%e 0,6,-15,40,-45,30,-8;

%e 0,7,-21,70,-105,105,-56,13;

%t Flatten[Table[Table[Sum[Binomial[n,j]Binomial[0,j-k]Fibonacci[j-2k],{j,0,n}],{k,0,n}],{n,0,10}],1]

%Y Cf. A094435.

%K easy,sign,tabl

%O 0,5

%A _Paul Barry_, Oct 11 2005

%E Values corrected and Mathematica program by _Olivier Gérard_, Oct 24 2012