A133938 Triangle read by rows: A007318 * (A129686 + A133080 - I) as infinite lower triangular matrices, where I is the identity matrix.

1, 2, 1, 4, 2, 1, 7, 4, 4, 1, 11, 8, 11, 4, 1, 16, 15, 25, 11, 6, 1, 22, 26, 50, 26, 22, 6, 1, 29, 42, 91, 56, 63, 22, 8, 1, 37, 64, 154, 112, 154, 64, 37, 8, 1, 46, 93, 246, 210, 336, 162, 129, 37, 10, 1, 56, 130, 375, 372, 672, 372, 375, 130, 56, 10, 1, 67, 176, 550, 627, 1254, 792, 957, 385, 231, 56, 12, 1

Offset

0,2

Comments

The matrix M = (A129686 + A133080 - I) is the tridiagonal matrix with (1,1,1,...) in the main diagonal, (1,0,1,0,...) in the subdiagonal and (1,1,1,...) in the subsubdiagonal.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Formula

From Andrew Howroyd, Sep 25 2025: (Start)

T(n,k) = binomial(n,k) + (binomial(n,k+1) + (-1)^k*binomial(n,k+1))/2 + binomial(n,k+2).

G.f.: (1 - (2 - y)*x + (2 - 2*y)*x^2 - (1 - 2*y)*x^3)/((1 - x)^2*(1 - (1 + y)*x)*(1 - (1 - y)*x)). (End)

Example

First few rows of the triangle:
   1;
   2,  1;
   4,  2,  1;
   7,  4,  4,  1;
  11,  8, 11,  4,  1;
  16, 15, 25, 11,  6,  1;
  22, 26, 50, 26, 22,  6,  1;
  ...

Crossrefs

Column 0 is A000124.

Row sums are A133124.

Cf. A007318, A129686, A133080.

Sequence in context: A316354 A104582 A209439 * A239829 A210034 A074586

Adjacent sequences: A133935 A133936 A133937 * A133939 A133940 A133941

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 29 2007

Extensions

Offset and a(47) corrected and a(55) onwards from Andrew Howroyd, Sep 25 2025

Status

approved