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

Author

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

Keywords

• easy
• nonn

Comments

Differences give A066368.

Examples

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

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

• 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).

Crossrefs

Cf. A092437-A092443.

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]