The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A003775

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A003775

Number of perfect matchings (or domino tilings) in P_5 X P_2n.
(history; published version)

#81 by Charles R Greathouse IV at Thu Sep 08 08:44:32 EDT 2022

PROG

(MAGMAMagma) I:=[1, 8, 95, 1183]; [n le 4 select I[n] else 15*Self(n-1)-32*Self(n-2)+15*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Aug 20 2018

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#80 by Michael De Vlieger at Sat Jan 15 09:49:42 EST 2022

STATUS

proposed

approved

#79 by Michel Marcus at Sat Jan 15 02:17:11 EST 2022

STATUS

editing

proposed

#78 by Michel Marcus at Sat Jan 15 02:17:03 EST 2022

LINKS

David Klarner, and Jordan Pollack, <a href="http://dx.doi.org/10.1016/0012-365X(80)90098-9">Domino tilings of rectangles with fixed width</a>, Disc. Math. 32 (1980) 45-52.

STATUS

proposed

editing

#77 by Jon E. Schoenfield at Sat Jan 15 00:27:07 EST 2022

STATUS

editing

proposed

#76 by Jon E. Schoenfield at Sat Jan 15 00:27:03 EST 2022

FORMULA

Limit_{n -> infinfinity} a(n)/a(n-1) = (3 + sqrt(5))*(5 + sqrt(21))/4 = 12.54375443458... - Philippe Deléham, Jun 13 2005

STATUS

proposed

editing

#75 by Jon E. Schoenfield at Fri Jan 14 23:34:16 EST 2022

STATUS

editing

proposed

#74 by Jon E. Schoenfield at Fri Jan 14 23:34:13 EST 2022

FORMULA

G.f.: (1-x)*(1 - 6*x + x^2)/(1 - 15*x + 32*x^2 - 15*x^3 + x^4).

Lim_Limit_{n -> Infinf} a(n)/a(n-1) = (3 + Sqrtsqrt(5))*(5 + Sqrtsqrt(21))/4 = 12.54375443458... - Philippe Deléham, Jun 13 2005

a(n) = ((35 + 7*sqrt(5) + 5*sqrt(21) + sqrt(105))*((3+sqrt(5))*(5+sqrt(21))/4)^n + (35 - 7*sqrt(5) + 5*sqrt(21) - sqrt(105))*((3-sqrt(5))*(5+sqrt(21))/4)^n + (35 + 7*sqrt(5) - 5*sqrt(21) - sqrt(105))*((3+sqrt(5))*(5-sqrt(21))/4)^n + (35 - 7*sqrt(5) - 5*sqrt(21) + sqrt(105))*((3-sqrt(5))*(5-sqrt(21))/4)^n)/140. [_- _Tim Monahan_, Aug 13 2011]

EXTENSIONS

Added recurrence Recurrence from Faase's web page. - _ added by _N. J. A. Sloane_, Feb 03 2009

STATUS

approved

editing

#73 by Andrew Howroyd at Tue May 19 12:04:30 EDT 2020

STATUS

reviewed

approved

#72 by Joerg Arndt at Tue May 19 11:38:13 EDT 2020

STATUS

proposed

reviewed