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A007787 Number of nonintersecting rook paths joining opposite corners of 5 X n board. 7

%I

%S 1,16,125,976,8512,79384,752061,7110272,67005561,630588698,5933085772,

%T 55827318685,525343024814,4943673540576,46521924780255,

%U 437788749723725,4119750109152730,38768318191017931,364823700357765771

%N Number of nonintersecting rook paths joining opposite corners of 5 X n board.

%D Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file (Science Section).

%H F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>

%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>

%H D. G. Radcliffe, N. J. A. Sloane, C. Cole, J. Gillogly, & D. Dodson, <a href="/A007765/a007765.pdf">Emails, 1994</a>

%F Faase gives a 27-term linear recurrence on his web page:

%F a(1) = 1,

%F a(2) = 16,

%F a(3) = 125,

%F a(4) = 976,

%F a(5) = 8512,

%F a(6) = 79384,

%F a(7) = 752061,

%F a(8) = 7110272,

%F a(9) = 67005561,

%F a(10) = 630588698,

%F a(11) = 5933085772,

%F a(12) = 55827318685,

%F a(13) = 525343024814,

%F a(14) = 4943673540576,

%F a(15) = 46521924780255,

%F a(16) = 437788749723725,

%F a(17) = 4119750109152730,

%F a(18) = 38768318191017931,

%F a(19) = 364823700357765771,

%F a(20) = 3433121323699285343,

%F a(21) = 32306898830469680384,

%F a(22) = 304019468350280601960,

%F a(23) = 2860931888452842047170,

%F a(24) = 26922391858409506569346,

%F a(25) = 253349332040459400463497,

%F a(26) = 2384107785665647075602841,

%F a(27) = 22435306570786253414376286 and

%F a(n) = 30a(n-1) - 383a(n-2) + 2772a(n-3) - 12378a(n-4) + 33254a(n-5)

%F - 40395a(n-6) - 44448a(n-7) + 239776a(n-8) - 274256a(n-9) - 180404a(n-10)

%F + 678758a(n-11) - 301650a(n-12) - 542266a(n-13) + 492472a(n-14) + 184306a(n-15)

%F - 225284a(n-16) - 102314a(n-17) + 25534a(n-18) + 97396a(n-19) + 10392a(n-20)

%F - 40292a(n-21) - 13218a(n-22) + 5328a(n-23) + 5376a(n-24) + 1822a(n-25)

%F + 319a(n-26) + 24a(n-27).

%F Asymptotics: a(n) ~ 0.115762181699251 * 9.4103574958247159212^n [From _Vaclav Kotesovec_, Aug 31 2012]

%Y Row 5 of A064298.

%Y Cf. A007764, A007786.

%K nonn,walk

%O 1,2

%A Heiner Marxen

%E More terms from _Ralf Stephan_, Mar 29 2004

%E Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009

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Last modified November 12 07:03 EST 2019. Contains 329052 sequences. (Running on oeis4.)