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

0,4

Comments

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

Links

Table of n, a(n) for n=0..65.

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

Example

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

Sequence in context: A325772 A226174 A208482 * A301906 A302150 A193554

Adjacent sequences: A199853 A199854 A199855 * A199857 A199858 A199859

Keyword

sign,tabl

Author

Philippe Deléham, Nov 11 2011

Status

approved