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

0,4

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).

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

Table of n, a(n) for n=0..35.

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.

Example

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

Crossrefs

Cf. A092438-A092443.

Sequence in context: A266681 A210664 A176093 * A064814 A051012 A064644

Adjacent sequences: A092434 A092435 A092436 * A092438 A092439 A092440

Keyword

hard,nonn,tabf,more

Author

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

Status

approved