A092438 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.

0, 2, 6, 26, 90, 302, 966, 3026, 9330, 28502, 86526, 261626, 788970, 2375102, 7141686, 21457826, 64439010, 193448102, 580606446, 1742343626, 5228079450, 15686335502, 47063200806, 141197991026, 423610750290, 1270865805302

Offset: 0

Author

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

Keywords

• easy
• nonn

Examples

			a(3) = (3^4+(-1)^4)/2-2^4+1 = 26.
		

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 (5,-5,-5,6).

Crossrefs

Cf. A046717, A092437-A092443, A140420.

Formula

a(n) = A092437(n, n+1).

a(n) = A046717(n+1)-2^(n+1)+1.

a(n) = (3^(n+1)+(-1)^(n+1))/2-2^(n+1)+1.

From R. J. Mathar, Apr 21 2010: (Start)

a(n) = +5*a(n-1) -5*a(n-2) -5*a(n-3) +6*a(n-4) = 2*A140420(n).

G.f.: -2*x*(1-2*x+3*x^2) / ( (x-1)*(3*x-1)*(2*x-1)*(1+x) ). (End)