A133366 Triangle T(n,k)read by rows given by [3,1,3,1,3,1,3,1,3,1,3,1,...] DELTA [1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

1, 3, 1, 12, 7, 1, 57, 43, 11, 1, 300, 262, 90, 15, 1, 1686, 1618, 667, 153, 19, 1, 9912, 10159, 4745, 1336, 232, 23, 1, 60213, 64783, 33147, 10785, 2333, 327, 27, 1, 374988, 418786, 229726, 83286, 21098, 3722, 438, 31, 1

Offset: 0

Author

Philippe Deléham, Oct 27 2007

Keywords

• nonn
• tabl

Comments

A121576*A007318 as infinite lower triangular matrices.

Examples

			Triangle begins:
       1;
       3,      1;
      12,      7,      1;
      57,     43,     11,     1;
     300,    262,     90,    15,     1;
    1686,   1618,    667,   153,    19,    1;
    9912,  10159,   4745,  1336,   232,   23,   1;
   60213,  64783,  33147, 10785,  2333,  327,  27,  1;
  374988, 418786, 229786, 83286, 21098, 3722, 438, 31, 1; ...
		

Crossrefs

Cf. A047891, A000012, A004767.

Cf. A007318, A121576.

Formula

T(0,0)=1; T(n,k) = 0 if k < 0 or if k > n; T(n,0) = 3*T(n-1,0) + 3*T(n-1,1); T(n,k) = T(n-1,k-1) + 4*T(n-1,k) + 3*T(n-1,k+1) for k >= 1.

Sum_{k>=0} T(m,k)*T(n,k)*3^k = T(m+n,0)= A047891(m+n+1). - Philippe Deléham, Jan 24 2010