A122837 Triangle T(n,k), 0<=k<=n, defined by : T(n,k)=0 if k<0, T(n,k)=0 if k>n,T(0,0)=1, T(1,0)=1, T(1,1)=-1, T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-2,k).

1, 1, -1, 2, 0, -1, 3, 1, -1, -1, 5, 4, -1, -2, -1, 8, 10, 2, -4, -3, -1, 13, 22, 11, -4, -8, -4, -1, 21, 45, 35, 3, -15, -13, -5, -1, 34, 88, 91, 34, -20, -32, -19, -6, -1, 55, 167, 214, 128, -1, -65, -56, -26, -7, -1

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Formula

Sum{k,0<=k<=n}T(n,k)=A000129(n-1)for n>0 .T(n,0) = Fibonacci(n+1)=A000045(n+1).

Example

Triangle begins:
1;
1, -1;
2, 0, -1;
3, 1, -1, -1;
5, 4, -1, -2, -1;
8, 10, 2, -4, -3, -1;
13, 22, 11, -4, -8, -4, -1;

Crossrefs

Sequence in context: A065432 A094184 A078805 * A143359 A291316 A130504

Adjacent sequences: A122834 A122835 A122836 * A122838 A122839 A122840

Keyword

sign,tabl

Author

Philippe Deléham, Oct 23 2006

Status

approved