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

0,2

Comments

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

A007318 + A000012 - A128174 as infinite lower triangular matrices.

Links

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

Example

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;
  ...

Prog

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

Crossrefs

Row sums are A134522.

Cf. A128174, A000012.

Sequence in context: A123275 A112544 A198789 * A131375 A358169 A327392

Adjacent sequences: A134518 A134519 A134520 * A134522 A134523 A134524

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 29 2007

Extensions

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

Status

approved