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

0,2

Comments

A121576*A007318 as infinite lower triangular matrices.

Links

Table of n, a(n) for n=0..44.

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

Example

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.

Sequence in context: A135888 A329433 A258245 * A049458 A143492 A375046

Adjacent sequences: A133363 A133364 A133365 * A133367 A133368 A133369

Keyword

nonn,tabl

Author

Philippe Deléham, Oct 27 2007

Status

approved