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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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 A243662

Adjacent sequences:  A133363 A133364 A133365 * A133367 A133368 A133369

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Oct 27 2007

STATUS

approved

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)