A092437 Triangle read by rows, arising from enumeration of domino tilings of Aztec Pillow-like regions.

1, 1, 1, 2, 1, 1, 5, 6, 6, 1, 1, 5, 13, 26, 30, 20, 1, 1, 5, 13, 41, 90, 140, 140, 70, 1, 1, 5, 13, 41, 121, 302, 560, 742, 630, 252

Offset: 0

Author

Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004

Keywords

• hard
• nonn
• tabf
• more
• changed

Comments

The rows are of lengths 1, 3, 5, 7, ...

Call the first row row 0 and entries starting from 0. Then entries i=0 through k in row k are A046717(i).

In row k, entry k+1 is sequence A092438 and entry k+2 is sequence A092439.

In row k, entry 2k-1 is A002457(k-1) and entry 2k is A000984(k).

Examples

			Triangle begins:
  1;
  1, 1, 2;
  1, 1, 5, 6, 6;
  1, 1, 5, 13, 26, 30, 20;
  ...
		

References

• James Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 13).

Links

• James Propp, Publications and Preprints.
• James Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics.

Crossrefs

Cf. A092438-A092443.