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

0,2

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]

Formula

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

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

G.f.: (x^18 -446x^17 +36701x^16 -1267416x^15 +22828288x^14 -235207768x^13 +1443564488x^12 -5338083112x^11 +11818867674x^10 -15460884436x^9 +11818867674x^8 -5338083112x^7 +1443564488x^6 -235207768x^5 +22828288x^4 -1267416x^3 +36701x^2 -446x +1)/(-x^19 +675x^18 -73471x^17 +3221189x^16 -72583272x^15 +925908264x^14 -6971103216x^13 +31523058272x^12 -86171526770x^11 +142604534086x^10 -142604534086x^9 +86171526770x^8 -31523058272x^7 +6971103216x^6 -925908264x^5 +72583272x^4 -3221189x^3 +73471x^2 -675x +1).

(End)

Crossrefs

Cf. A006253, A028454, A049507.

Sequence in context: A124684 A332740 A178673 * A072020 A177826 A122269

Adjacent sequences: A028449 A028450 A028451 * A028453 A028454 A028455

Keyword

nonn

Author

Per H. Lundow

Status

approved