A092439 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.

0, 0, 6, 30, 140, 560, 2058, 7098, 23472, 75372, 237182, 735878, 2260596, 6896136, 20933778, 63325170, 191089112, 575626052, 1731858246, 5206059774, 15640198620, 46966732320, 140996664986, 423191320490, 1269993390720

Offset

0,3

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..24.

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 (9,-30,42,-9,-39,40,-12).

Formula

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

a(n) = Entry n+2 in row n of (Sequence to be added #1).

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

a(n) = 9*a(n-1)-30*a(n-2)+42*a(n-3)-9*a(n-4)-39*a(n-5)+40*a(n-6)-12*a(n-7). [Harvey P. Dale, Nov 27 2011]

G.f.: 2*x^2*(6*x^4-26*x^3+25*x^2-12*x+3)/((x-1)^3*(x+1)*(2*x-1)^2*(3*x-1)). [Colin Barker, Nov 22 2012]

Example

a(3)=(3^5+(-1)^5)/2-2^5-5(2^4-1)+4^2=30.

Mathematica

Table[(3^(n+2)+(-1)^(n+2))/2-2^(n+2)-(n+2)(2^(n+1)-1)+(n+1)^2, {n, 0, 30}] (* or *) LinearRecurrence[{9, -30, 42, -9, -39, 40, -12}, {0, 0, 6, 30, 140, 560, 2058}, 30] (* Harvey P. Dale, Nov 27 2011 *)

Crossrefs

Cf. A092437-A092443.

Sequence in context: A192208 A001334 A125316 * A082149 A002457 A137400

Adjacent sequences: A092436 A092437 A092438 * A092440 A092441 A092442

Keyword

easy,nonn

Author

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

Status

approved