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A007787 Number of nonintersecting rook paths joining opposite corners of 5 X n board. +0
5
1, 16, 125, 976, 8512, 79384, 752061, 7110272, 67005561, 630588698, 5933085772, 55827318685, 525343024814, 4943673540576, 46521924780255, 437788749723725, 4119750109152730, 38768318191017931, 364823700357765771 (list; graph; listen)
OFFSET

1,2

REFERENCES

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

LINKS

F. Faase, Counting Hamilton cycles in product graphs

F. Faase, Results from the counting program

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).

CROSSREFS

Cf. A007786.

Sequence in context: A126511 A067442 A000485 this_sequence A067470 A133111 A163399

Adjacent sequences: A007784 A007785 A007786 this_sequence A007788 A007789 A007790

KEYWORD

nonn,walk

AUTHOR

Heiner Marxen

EXTENSIONS

More terms from R. Stephan, Mar 29 2004

Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009

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Last modified November 24 14:25 EST 2009. Contains 167438 sequences.


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