A198793 Triangle T(n,k), read by rows, given by (1,0,0,1,0,0,0,0,0,0,0,...) DELTA (0,1,1,0,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 6, 4, 0, 1, 4, 12, 16, 8, 0, 1, 5, 20, 40, 40, 16, 0, 1, 6, 30, 80, 120, 96, 32, 0, 1, 7, 42, 140, 280, 336, 224, 64, 0, 1, 8, 56, 224, 560, 896, 896, 512, 128, 0, 1, 9, 72, 336, 1008, 2016, 2688, 2304, 1152, 256, 0

Offset

0,8

Comments

Mirror image of A198792.

Variant of A082137.

Links

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

Formula

Sum_ {0<=k<=n} T(n,k) = A124302(n).

G.f.:(1-x*(1+2y)+x^2*y)/((1-x)*(1-(1+2y)*x)).

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1) for n>2, T(0,0) = T(1,0) = T(2,0) = T(2,1) = 1, T(1,1) = T(2,2) = 0, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 10 2013

Example

Triangle begins :
1
1, 0
1, 1, 0
1, 2, 2, 0
1, 3, 6, 4, 0
1, 4, 12, 16, 8, 0,
1, 5, 20, 40, 40, 16, 0

Crossrefs

Cf. A082137, A084938, A198792.

Sequence in context: A091063 A246935 A342120 * A085388 A351339 A361432

Adjacent sequences: A198790 A198791 A198792 * A198794 A198795 A198796

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Oct 30 2011

Status

approved