A028448 Number of perfect matchings in graph P_{2} X P_{4} X P_{n}.

1, 5, 121, 1845, 32000, 535229, 9049169, 152526845, 2573281769, 43402320448, 732106008249, 12348802743437, 208295014563521, 3513435627771565, 59263242055245056, 999628735946792581, 16861339891166667849, 284410369641222811445, 4797320930581855672689

Offset: 0

Author

Per H. Lundow

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..800
• 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.

Crossrefs

Column k=4 of A181206.

Formula

G.f.: (-x^19 +17*x^18 -53*x^17 -383*x^16 +2051*x^15 +1155*x^14 -16891*x^13 +9523*x^12 +45157*x^11 -41065*x^10 -41065*x^9 +45157*x^8 +9523*x^7 -16891*x^6 +1155*x^5 +2051*x^4 -383*x^3 -53*x^2 +17*x -1) / (x^21 -22*x^20 +42*x^19 +990*x^18 -3493*x^17 -12199*x^16 +55858*x^15 +27106*x^14 -289337*x^13 +146481*x^12 +488514*x^11 -488514*x^10 -146481*x^9 +289337*x^8 -27106*x^7 -55858*x^6 +12199*x^5 +3493*x^4 -990*x^3 -42*x^2 +22*x -1). - Alois P. Heinz, Dec 08 2013