A028452 Number of perfect matchings in graph P_{3} X P_{3} X P_{2n}.

1, 229, 117805, 64647289, 35669566217, 19690797527709, 10870506600976757, 6001202979497804657, 3313042830624031354513, 1829008840116358153050197, 1009728374600381843221483965, 557433823481589253332775648233, 307738670509229621147710358375321

Offset: 0

Author

Per H. Lundow

Keywords

• nonn

Comments

Also the number of tilings of a 3 x 3 x 2n box with 1 x 1 x 2 bricks. - Johan de Ruiter, Jul 15 2012

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• Per Hakan Lundow, Computation of matching polynomials and the number of 1-factors in polygraphs, Research report, No 12, 1996, Department of Math., Umea University, Sweden.
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
• R. J. Mathar, Tilings of rectangular regions by rectangular tiles: Counts derived from transfer matrices, arXiv:1406.7788 [math.CO], (2014), eq (38).
• James Propp, A reciprocity theorem for domino tilings, El. J. Combin. 8 (2001) #R18.
• J. de Ruiter, Counting Domino Coverings and Chessboard Cycles, 2010. [Broken link]

Crossrefs

Cf. A006253, A028454, A049507.

Formula

From Johan de Ruiter, Jul 15 2012: (Start)

a(n) = 679a(n-1) -76177a(n-2) +3519127a(n-3) -85911555a(n-4) [phone]a(n-5) -11123194131a(n-6) [phone]a(n-7) -257866595482a(n-8) [phone]a(n-9) -1363115167354a(n-10) [phone]a(n-11) -1888426032982a(n-12) [phone]a(n-13) -705239311926a(n-14) [phone]a(n-15) -65256474997a(n-16) [phone]a(n-17) -1235863045a(n-18) [phone]a(n-19) -3519127a(n-20) +76177a(n-21) -679a(n-22) +a(n-23).

G.f.: (x^18 -446x^17 +36701x^16 -1267416x^15 [phone]x^14 -235207768x^13 [phone]x^12 -5338083112x^11 [phone]x^10 -15460884436x^9 [phone]x^8 -5338083112x^7 [phone]x^6 -235207768x^5 [phone]x^4 -1267416x^3 +36701x^2 -446x +1)/(-x^19 +675x^18 -73471x^17 +3221189x^16 -72583272x^15 [phone]x^14 -6971103216x^13 [phone]x^12 -86171526770x^11 [phone]x^10 -142604534086x^9 [phone]x^8 -31523058272x^7 [phone]x^6 -925908264x^5 [phone]x^4 -3221189x^3 +73471x^2 -675x +1).

(End)