A092442 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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.