A347679 Irregular triangle read by rows: T(n,k) (1 <= k <= 2*n) = number of n X k Baxter matrices in which all row sums are 2.

0, 1, 0, 0, 2, 4, 0, 0, 0, 3, 24, 26, 0, 0, 0, 0, 8, 98, 284, 214, 0, 0, 0, 0, 0, 19, 374, 1922, 3496, 2030, 0, 0, 0, 0, 0, 0, 44, 1342, 10620, 33398, 44674, 21174, 0, 0, 0, 0, 0, 0, 0, 111, 4596, 51904, 245684, 554500, 589092, 236410

Offset

1,5

Links

Table of n, a(n) for n=1..56.

Don Knuth, Baxter matrices, Preprint, Sep 05 2021.

Example

The T(4,5)=8 matrices of size 4 X 5 are
.
  0 0 0 1 1   0 0 0 1 1   0 1 0 0 1   1 0 0 0 1
  0 0 1 1 0   1 0 0 1 0   0 0 1 1 0   0 0 1 1 0
  0 1 1 0 0   0 1 1 0 0   0 1 0 0 1   0 1 1 0 0
  1 1 0 0 0   1 0 0 1 0   1 1 0 0 0   1 0 0 0 1
.
  1 0 0 0 1   1 0 0 1 0   1 1 0 0 0   1 1 0 0 0
  0 1 1 0 0   0 1 1 0 0   0 1 0 0 1   0 1 1 0 0
  0 0 1 1 0   1 0 0 1 0   0 0 1 1 0   0 0 1 1 0
  1 0 0 0 1   0 0 0 1 1   0 1 0 0 1   0 0 0 1 1

Crossrefs

Cf. A347678, A347736 (superdiagonal).

Sequence in context: A107501 A126732 A371648 * A028586 A253179 A300723

Adjacent sequences: A347676 A347677 A347678 * A347680 A347681 A347682

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Sep 10 2021

Status

approved