A145974 -id:A145974 - cp's OEIS frontend

A145973 Triangle read by rows, square of A053121.

1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 7, 0, 6, 0, 1, 0, 18, 0, 8, 0, 1, 29, 0, 33, 0, 10, 0, 1, 0, 86, 0, 52, 0, 12, 0, 1, 131, 0, 179, 0, 75, 0, 14, 0, 1, 0, 427, 0, 316, 0, 102, 0, 16, 0, 1, 625, 0, 972, 0, 505, 0, 133, 0, 18, 0, 1

Offset: 0

Gary W. Adamson and Roger L. Bagula, Oct 25 2008

Left border = aerated version of A007852.

			First few rows of the triangle:
    1;
    0,   1;
    2,   0,   1;
    0,   4,   0,   1;
    7,   0,   6,   0,   1;
    0,  18,   0,   8,   0,   1;
   29,   0,  33,   0,  10,   0,   1;
    0,  86,   0,  52,   0,  12,   0,   1;
  131,   0, 179,   0,  75,   0,  14,   0,   1;
    0, 427,   0, 316,   0, 102,   0,  16,   0,   1;
  625,   0, 972,   0, 505,   0, 133,   0,  18,   0,   1;
  ...

Cf. A053121.
Cf. A007852, A145974 (row sums).
This triangle is the square of A053121.

A145973 := proc(n,k)
    add(A053121(n,j)*A053121(j,k),j=k..n) ;
end proc: # R. J. Mathar, Mar 03 2013

Triangle read by rows, A053121^2.

A153585 Convolution triangle, A053121 * (A001405 * 0^(n-k)).

Original entry on oeis.org

1, 0, 1, 1, 0, 2, 0, 2, 0, 3, 2, 0, 6, 0, 6, 0, 5, 0, 12, 0, 10, 5, 0, 18, 0, 30, 0, 20, 0, 14, 0, 42, 0, 60, 0, 35, 14, 0, 56, 0, 120, 0, 140, 0, 70, 0, 42, 0, 144, 0, 270, 0, 280, 0, 126

Offset: 0

Gary W. Adamson, Dec 28 2008

Row sums = A145974: (1, 1, 3, 5, 14, 27, 73,...).

			First few rows of the triangle =
1;
0, 1;
1, 0, 2;
0, 2, 0, 3;
2, 0, 6, 0, 6;
0, 5, 0, 12, 0, 10;
5, 0, 18, 0, 30, 0, 20;
0, 14, 0, 42, 0, 60, 0, 35;
14, 0, 56, 0, 120, 0, 140, 0, 70;
0, 42, 0, 144, 0, 270, 0, 280, 0, 126;
42, 0, 180, 0, 450, 0, 700, 0, 630, 0, 252;
...
Example: Row 4 = (2, 0, 6, 0, 6) = termwise products of (2, 0, 3, 0, 1) and (1, 1, 2, 3, 6).

Convolution triangle, A053121 * (A001405 * 0^(n-k)).
A053121 = the aerated Catalan triangle and (A001405 * 0^(n-k) = an
infinite lower triangular matrix with A001405 as the main diagonal and
the rest zeros.

cp's OEIS Frontend

A145973 Triangle read by rows, square of A053121.

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