A133366 - OEIS

%I #12 Jan 25 2020 02:29:47

%S 1,3,1,12,7,1,57,43,11,1,300,262,90,15,1,1686,1618,667,153,19,1,9912,

%T 10159,4745,1336,232,23,1,60213,64783,33147,10785,2333,327,27,1,

%U 374988,418786,229726,83286,21098,3722,438,31,1

%N 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.

%C A121576*A007318 as infinite lower triangular matrices.

%F 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.

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

%e Triangle begins:

%e        1;

%e        3,      1;

%e       12,      7,      1;

%e       57,     43,     11,     1;

%e      300,    262,     90,    15,     1;

%e     1686,   1618,    667,   153,    19,    1;

%e     9912,  10159,   4745,  1336,   232,   23,   1;

%e    60213,  64783,  33147, 10785,  2333,  327,  27,  1;

%e   374988, 418786, 229786, 83286, 21098, 3722, 438, 31, 1; ...

%Y Cf. A047891, A000012, A004767.

%Y Cf. A007318, A121576.

%K nonn,tabl

%O 0,2

%A _Philippe Deléham_, Oct 27 2007