A130302 -id:A130302 - cp's OEIS frontend

A131414 A130302 + A130303 - A000012.

1, 5, 1, 10, 3, 1, 16, 5, 3, 1, 23, 7, 5, 3, 1, 31, 9, 7, 5, 3, 1, 40, 11, 9, 7, 5, 3, 1, 50, 13, 11, 9, 7, 5, 3, 1, 61, 15, 13, 11, 9, 7, 5, 3, 1, 73, 17, 15, 13, 11, 9, 7, 5, 3, 1

Offset: 1

Gary W. Adamson, Jul 08 2007

Left column = A052905: (1, 5, 10, 16, 23, 31,...). Row sums = A095794: (1, 6, 14, 25, 39,...).

			First few rows of the triangle are:
1;
5, 1;
10, 3, 1;
16, 5, 3, 1;
23, 7, 5, 3, 1;
31, 9, 7, 5, 3, 1;
...

Cf. A130302, A130303, A052905, A095794.

A130302 + A130303 - A000012 as infinite lower triangular matrices.

A130303 A130296 * A000012.

Original entry on oeis.org

1, 3, 1, 5, 2, 1, 7, 3, 2, 1, 9, 4, 3, 2, 1, 11, 5, 4, 3, 2, 1, 13, 6, 5, 4, 3, 2, 1, 15, 7, 6, 5, 4, 3, 2, 1, 17, 8, 7, 6, 5, 4, 3, 2, 1, 19, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Gary W. Adamson, May 20 2007

			1;
3, 1;
5, 2, 1;
7, 3, 2, 1;
9, 4, 3, 2, 1;
11, 5, 4, 3, 2, 1;
13, 6, 5, 4, 3, 2, 1;
15, 7, 6, 5, 4, 3, 2, 1;
17, 8, 7, 6, 5, 4, 3, 2, 1;
19, 9, 8, 7, 6, 5, 4, 3, 2, 1;

H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162

Cf. A130296, A000012, A034856 (row sums), A130302 (commuted matrix product)

Clear[e, n, k];
e[n_, 0] := 2*n - 1;
e[n_, k_] := 0 /; k >= n;
e[n_, k_] := (e[n - 1, k]*e[n, k - 1] + 1)/e[n - 1, k - 1];
Table[Table[e[n, k], {k, 0, n - 1}], {n, 1, 10}];
Flatten[%]

A130296 * A000012 as infinite lower triangular matrices. (1,3,5,...) as the left border; (1,2,3,...) in all other columns.

e(n,k)= (e(n - 1, k)*e(n, k - 1) + 1)/e(n - 1, k - 1)

Additional comments from Roger L. Bagula and Gary W. Adamson, Mar 28 2009

cp's OEIS Frontend

A131414 A130302 + A130303 - A000012.

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A130303 A130296 * A000012.

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