A092442 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.

0, 1, 5, 19, 59, 161, 405, 967, 2231, 5029, 11153, 24443, 53091, 114505, 245549, 524047, 1113839, 2358989, 4980393, 10485379, 22019675, 46136881, 96468485, 201326039, 419429799, 872414581, 1811938625, 3758095627, 7784627411

Offset

0,3

Comments

Differences give A066368.

References

J. 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..28.

J. Propp, Publications and Preprints

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

Index entries for linear recurrences with constant coefficients, signature (7,-19,25,-16,4).

Formula

a(n)=(n+1)(2^n-1)-n^2.

G.f.:(x*(4*x^3-3*x^2+2*x-1))/((2*x-1)^2*(x-1)^3) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]

Example

a(3)=4(2^3-1)-3^2=19.

Crossrefs

Cf. A092437-A092443.

Sequence in context: A224034 A107179 A332720 * A341711 A328543 A135266

Adjacent sequences: A092439 A092440 A092441 * A092443 A092444 A092445

Keyword

easy,nonn

Author

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

Status

approved