OFFSET
0,6
COMMENTS
T(n,n) is A001045(n), row sums are A006130, column sums are A002605. Compare with [0,1,-1,0,0,..] DELTA [1,2,-2,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-x-2x^2),x/(1-x-2x^2)) (A073370).
Modulo 2, this sequence gives A106344. - Philippe Deléham, Dec 18 2008
FORMULA
From Philippe Deléham: (Start)
G.f.: 1/(1-yx(1-x)-2x^2*y*2);
Number triangle T(n, k) = Sum_{j=0..2k-n} C(n-k+j, n-k)*C(j, 2k-n-j)*2^(2k-n-j);
T(n, k) = A073370(k, n-k); T(n, k) = T(n-1, k-1) + T(n-2, k-1) + 2*T(n-2, k-2). (End)
EXAMPLE
Rows begin
1;
0, 1;
0, 1, 3;
0, 0, 2, 5;
0, 0, 1, 7, 11;
0, 0, 0, 3, 16, 21;
0, 0, 0, 1, 12, 41, 43;
0, 0, 0, 0, 4, 34, 94, 85;
0, 0, 0, 0, 1, 18, 99, 219, 171;
0, 0, 0, 0, 0, 5, 60, 261, 492, 341;
0, 0, 0, 0, 0, 1, 25, 195, 678, 1101, 683;
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Oct 05 2005
STATUS
approved