A133805 Triangle read by rows: A007318 * A133566 * A133080.

1, 2, 1, 4, 3, 1, 7, 6, 4, 1, 11, 10, 11, 5, 1, 16, 15, 25, 15, 6, 1, 22, 21, 50, 35, 22, 7, 1, 29, 28, 91, 70, 63, 28, 8, 1, 37, 36, 154, 126, 154, 84, 37, 9, 1, 46, 45, 246, 210, 336, 210, 129, 45, 10, 1, 56, 55, 375, 330, 672, 462, 375, 165, 56, 11, 1, 67, 66, 550, 495, 1254, 924, 957, 495, 231, 66, 12, 1

Offset

1,2

Comments

Row sums = A133806: (1, 3, 8, 18, 38, 78, 318, ...).

Left column = A000124.

Links

Table of n, a(n) for n=1..78.

Formula

Binomial transform of (A133566 * A133080) where (A133566 * A133080) = an infinite lower triangular matrix with (1,1,1,...) in the main and subdiagonals and (1,0,1,0,1,...) in the subsubdiagonal.

Example

First few rows of the triangle:
   1;
   2,  1;
   4,  3,  1;
   7,  6,  4,  1;
  11, 10, 11,  5,  1;
  16, 15, 25, 15,  6,  1;
  22, 21, 50, 35, 22,  7,  1;
  29, 28, 91, 70, 63, 28,  8,  1;
  ...

Crossrefs

Cf. A000124, A133080, A133566, A133804, A133806.

Sequence in context: A027421 A131252 A345123 * A131254 A210229 A210213

Adjacent sequences: A133802 A133803 A133804 * A133806 A133807 A133808

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 23 2007

Extensions

a(21) = 1 inserted and more terms from Georg Fischer, Jun 08 2023

Status

approved