1,5

Each row of the triangle is a palindrome.

Let M = the Narayana (or Catalan) triangle, A001263 as an infinite lower triangular matrix. Generate an array by rows, taking the product (M * V); where V = rows of the Narayana triangle considered as vectors. Rows of the triangle are antidiagonals of the array.

First few rows of the array are:

1, 1, 1, 1, 1,...

1, 2, 4, 7, 11,...

1, 4, 11, 25, 51,...

1, 7, 25, 74, 191,...

1, 11, 51, 191, 602,...

...

n-th row of the array is generated from (M * V), where V in turn = n-th row of the Narayana triangle: (1); (1, 1); (1, 3, 1), (1, 6, 6, 1)...(i.e., terms followed by zeros to form a vector, as (1, 3, 1, 0, 0, 0...). Example: T(6,3) and T(6,4) = 25 = 1*0 + 1*1 + 6*1 + 6*18 = 0+1+6+18 = 25.

First few rows of the triangle are:

1;

1, 1;

1, 2, 1;

1, 4, 4, 1;

1, 7, 11, 7, 1;

1, 11, 25, 25, 11, 1;

1, 16, 51, 74, 51, 16, 1;

1, 22, 96, 191, 191, 96, 22, 1;

...

Cf. A001263.

Sequence in context: A128562 A034368 A113582 this_sequence A104382 A086629 A126770

Adjacent sequences: A118242 A118243 A118244 this_sequence A118246 A118247 A118248

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2006