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 A003779 Number of spanning trees in P_5 x P_n. 3
 1, 209, 30305, 4140081, 557568000, 74795194705, 10021992194369, 1342421467113969, 179796299139278305, 24080189412483072000, 3225041354570508955681, 431926215138756947267505, 57847355494807961811035009, 7747424602888405489208931601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also number of domino tilings of the 9 X (2n-1) rectangle with upper left corner removed. - Alois P. Heinz, Apr 14 2011 REFERENCES F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154. LINKS P. Raff, Table of n, a(n) for n = 1..200 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154. F. Faase, Results from the counting program P. Raff, Spanning Trees in Grid Graphs. [Added by Paul Raff, Oct 30 2009] P. Raff, Analysis of the Number of Spanning Trees of P_5 x P_n. Contains sequence, recurrence, generating function, and more. [Added by Paul Raff, Oct 30 2009] P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs. [Added by Paul Raff, Oct 30 2009] FORMULA a(n) = 209 a(n-1) - 11936 a(n-2) + 274208 a(n-3) - 3112032 a(n-4) + 19456019 a(n-5) - 70651107 a(n-6) + 152325888 a(n-7) - 196664896 a(n-8) + 152325888 a(n-9) - 70651107 a(n-10) + 19456019 a(n-11) - 3112032 a(n-12) + 274208 a(n-13) - 11936 a(n-14) + 209 a(n-15) - a(n-16) [Modified by Paul Raff, Oct 30, 2009] G.f.: -x(x^14-1440x^12+26752x^11 -185889x^10+574750x^9-708928x^8 +708928x^6-574750x^5+185889x^4 -26752x^3+1440x^2-1) / (x^16-209x^15 +11936x^14 -274208x^13+3112032x^12-19456019x^11 +70651107x^10 -152325888x^9 +196664896x^8 -152325888x^7+70651107x^6 -19456019x^5 +3112032x^4-274208x^3+11936x^2-209x+1). CROSSREFS A row of A116469. Bisection of A189005. Sequence in context: A203040 A029554 A203458 * A071379 A125549 A104876 Adjacent sequences:  A003776 A003777 A003778 * A003780 A003781 A003782 KEYWORD nonn AUTHOR EXTENSIONS Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009 STATUS approved

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Last modified May 23 08:33 EDT 2013. Contains 225585 sequences.