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

0,2

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..25.

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).

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)

Example

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

Crossrefs

Cf. A046717, A092437-A092443, A140420.

Sequence in context: A223094 A213339 A317867 * A240296 A027207 A027231

Adjacent sequences: A092435 A092436 A092437 * A092439 A092440 A092441

Keyword

easy,nonn

Author

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

Status

approved