A198792 Triangle T(n,k), read by rows, given by (0,1,1,0,0,0,0,0,0,0,...) DELTA (1,0,0,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

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

Offset

0,8

Comments

Row sums are A124302.

Variant of A119468.

Links

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

Formula

T(n,k) = A097805(n,k)*A011782(n-k).

Sum_{0<=k<=n} T(n,k)*2^k = A063376(n-1).

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

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

Example

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

Crossrefs

Columns include A000007, A011782, A057711, A080929, A082138, A080951, A082139, A082140, A082141, A000012, A001477, A002378.

Sequence in context: A062110 A122896 A191348 * A196182 A107267 A320530

Adjacent sequences: A198789 A198790 A198791 * A198793 A198794 A198795

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Oct 30 2011

Status

approved