

A134521


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


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
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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 are:
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 A327392 A112798
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



