A092441 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.

1, 10, 65, 346, 1637, 7218, 30529, 126034, 513125, 2072698, 8335505, 33439914, 133972165, 536346850, 2146369793, 8587575586, 34354757957, 137428468074, 549733794193, 2198977118650, 8795996553701, 35184170762770

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..21.

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 (11,-47,101,-116,68,-16).

Formula

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

G.f.: -(8*x^4-2*x^2+x-1)/((x-1)^3*(2*x-1)^2*(4*x-1)). [Colin Barker, Nov 22 2012]

Example

a(3) = 2^9-2^5-10(2^4-1)+4^2 = 346.

Mathematica

LinearRecurrence[{11, -47, 101, -116, 68, -16}, {1, 10, 65, 346, 1637, 7218}, 30] (* Harvey P. Dale, Nov 26 2022 *)

Crossrefs

Cf. A092437-A092443.

Sequence in context: A023009 A169797 A073381 * A022638 A354393 A346976

Adjacent sequences: A092438 A092439 A092440 * A092442 A092443 A092444

Keyword

easy,nonn

Author

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

Status

approved