A113020 Number triangle whose row sums are the Fibonacci numbers.

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, -8, 0, 7, -21, 70, -105, 105, -56, 13, 0, 8, -28, 112, -210, 280, -224, 104, -21, 0, 9, -36, 168, -378, 630, -672, 468, -189, 34, 0, 10, -45, 240, -630, 1260, -1680, 1560, -945, 340, -55

Offset: 0

Author

Paul Barry, Oct 11 2005

Keywords

• easy
• sign
• tabl

Comments

Row sums sequence is A000045, F(n).

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

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

Diagonal sums are A113021.

Examples

			Rows begin
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,-8;
0,7,-21,70,-105,105,-56,13;
		

Links

• Olivier Gérard, Table of n, a(n) for n = 0..230

Crossrefs

Cf. A094435.

Programs

Mathematica

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

Formula

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

Extensions

Values corrected and Mathematica program by Olivier Gérard, Oct 24 2012