login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 to sequences with 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 22 10:43 EST 2014. Contains 249805 sequences.