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A092439 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A092439(n) = Entry n+2 in row n of (Sequence to be added #1).

A092439(n) = A046717(n+2)-2^(n+2)-(n+2)(2^(n+1)-1)+(n+1)^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..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(0)=0, a(1)=0, a(2)=6, a(3)=30, a(4)=140, a(5)=560, a(6)=2058, 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) [From 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

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Last modified December 8 15:08 EST 2016. Contains 278945 sequences.