A134521 Triangle read by rows: T(n,k) = binomial(n,k) + (n + k) mod 2.

1, 2, 1, 1, 3, 1, 2, 3, 4, 1, 1, 5, 6, 5, 1, 2, 5, 11, 10, 6, 1, 1, 7, 15, 21, 15, 7, 1, 2, 7, 22, 35, 36, 21, 8, 1, 1, 9, 28, 57, 70, 57, 28, 9, 1, 2, 9, 37, 84, 127, 126, 85, 36, 10, 1, 1, 11, 45, 121, 210, 253, 210, 121, 45, 11, 1, 2, 11, 56, 165, 331, 462, 463, 330, 166, 55, 12, 1

Offset: 0

Author

Gary W. Adamson, Oct 29 2007

Keywords

• nonn
• tabl

Comments

Row sums = A134522: (1, 3, 5, 10, 18, 35, 67, ...).

A007318 + A000012 - A128174 as infinite lower triangular matrices.

Examples

			First few rows of the triangle:
  1;
  2,  1;
  1,  3,  1;
  2,  3,  4,  1;
  1,  5,  6,  5,  1;
  2,  5, 11, 10,  6,  1;
  1,  7, 15, 21, 15,  7,  1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1274

Crossrefs

Row sums are A134522.

Cf. A128174, A000012.

Programs

PARI

T(n,k)=if(k<=n, binomial(n,k) + (n+k)%2, 0) \\ Andrew Howroyd, Aug 10 2018

Extensions

Name changed and a(39) corrected by Andrew Howroyd, Aug 10 2018