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 A007787 Number of nonintersecting rook paths joining opposite corners of 5 X n board. 7
 1, 16, 125, 976, 8512, 79384, 752061, 7110272, 67005561, 630588698, 5933085772, 55827318685, 525343024814, 4943673540576, 46521924780255, 437788749723725, 4119750109152730, 38768318191017931, 364823700357765771 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file (Science Section). LINKS F. Faase, Results from the counting program D. G. Radcliffe, N. J. A. Sloane, C. Cole, J. Gillogly, & D. Dodson, Emails, 1994 FORMULA Faase gives a 27-term linear recurrence on his web page: a(1) = 1, a(2) = 16, a(3) = 125, a(4) = 976, a(5) = 8512, a(6) = 79384, a(7) = 752061, a(8) = 7110272, a(9) = 67005561, a(10) = 630588698, a(11) = 5933085772, a(12) = 55827318685, a(13) = 525343024814, a(14) = 4943673540576, a(15) = 46521924780255, a(16) = 437788749723725, a(17) = 4119750109152730, a(18) = 38768318191017931, a(19) = 364823700357765771, a(20) = 3433121323699285343, a(21) = 32306898830469680384, a(22) = 304019468350280601960, a(23) = 2860931888452842047170, a(24) = 26922391858409506569346, a(25) = 253349332040459400463497, a(26) = 2384107785665647075602841, a(27) = 22435306570786253414376286 and a(n) = 30a(n-1) - 383a(n-2) + 2772a(n-3) - 12378a(n-4) + 33254a(n-5) - 40395a(n-6) - 44448a(n-7) + 239776a(n-8) - 274256a(n-9) - 180404a(n-10) + 678758a(n-11) - 301650a(n-12) - 542266a(n-13) + 492472a(n-14) + 184306a(n-15) - 225284a(n-16) - 102314a(n-17) + 25534a(n-18) + 97396a(n-19) + 10392a(n-20) - 40292a(n-21) - 13218a(n-22) + 5328a(n-23) + 5376a(n-24) + 1822a(n-25) + 319a(n-26) + 24a(n-27). Asymptotics: a(n) ~ 0.115762181699251 * 9.4103574958247159212^n [From Vaclav Kotesovec, Aug 31 2012] CROSSREFS Row 5 of A064298. Cf. A007764, A007786. Sequence in context: A000485 A264625 A213748 * A067470 A133111 A268998 Adjacent sequences:  A007784 A007785 A007786 * A007788 A007789 A007790 KEYWORD nonn,walk AUTHOR Heiner Marxen EXTENSIONS More terms from Ralf Stephan, Mar 29 2004 Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)