A199856 Triangle T(n,k), read by rows, given by (-1,3,0,0,0,0,0,0,0,0,0,...) DELTA (1,0,-1/3,1/3,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, -1, 1, -2, 1, 1, -4, 1, 2, 1, -8, 0, 4, 3, 1, -16, -4, 7, 8, 4, 1, -32, -16, 10, 19, 13, 5, 1, -64, -48, 8, 41, 37, 19, 6, 1, -128, -128, -16, 80, 96, 62, 26, 7, 1, -256, -320, -112, 136, 231, 183, 95, 34, 8, 1, -512, -768, -416, 176, 518, 501, 311, 137, 43, 9, 1

Offset: 0

Author

Philippe Deléham, Nov 11 2011

Keywords

• sign
• tabl

Comments

Diagonal sums are in A199853, row sums are in A000007.

Examples

			Triangle begins :
1
-1, 1
-2, 1, 1
-4, 1, 2, 1
-8, 0, 4, 3, 1
-16, -4, 7, 8, 4, 1
-32, -16, 10, 19, 13, 5, 1
-64, -48, 8, 41, 37, 19, 6, 1
-128, -128, -16, 80, 96, 62, 26, 7, 1
		

Crossrefs

Cf. A000012, A000079

Formula

T(n,k)=2*T(n-1,k)+T(n-1,k-1)-T(n-2,k-1), for n>2.

T(n,0)=-2^(n-1) for n>0.

T(2*n,n)=A047781(n) for n>0.

T(n,1)=(4-n)*2^(n-3) for n>1.

G.f.: (1-3*x+x^2*y)/(1-2*x+x^2*y-x*y). - R. J. Mathar, Aug 11 2015