The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A186857 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A186857

Number of 8-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.
(history; published version)

#14 by Michael De Vlieger at Mon Jan 02 21:56:31 EST 2023

STATUS

proposed

approved

#13 by Andrew Howroyd at Mon Jan 02 17:17:29 EST 2023

STATUS

editing

proposed

#12 by Andrew Howroyd at Mon Jan 02 16:10:26 EST 2023

DATA

16, 2208, 57392, 405040, 1508784, 3846192, 7777808, 13502064, 21089312, 30521216, 41748432, 54726992, 69434272, 85865344, 104020208, 123898864, 145501312, 168827552, 193877584, 220651408, 249149024, 279370432, 311315632, 344984624, 380377408, 417493984

COMMENTS

Row 8 of A186851.

LINKS

Andrew Howroyd, <a href="/A186857/b186857.txt">Table of n, a(n) for n = 1..1000</a>

FORMULA

a(n) = 861896*n^2 - 6840120*n + 12695408 for n >= 12. - Andrew Howroyd, Jan 02 2023

PROG

(PARI) row(8, 30) \\ row(m, n) defined in A186851. - Andrew Howroyd, Jan 02 2023

CROSSREFS

Row 8 of A186851.

KEYWORD

nonn,more,changed

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, Jan 02 2023

STATUS

approved

editing

#11 by Joerg Arndt at Sun Jan 01 03:21:31 EST 2023

STATUS

reviewed

approved

#10 by Michel Marcus at Sun Jan 01 03:09:11 EST 2023

STATUS

proposed

reviewed

#9 by Michel Marcus at Sun Jan 01 03:09:03 EST 2023

STATUS

editing

proposed

#8 by Michel Marcus at Sun Jan 01 03:09:00 EST 2023

KEYWORD

nonn,more,changed

STATUS

reviewed

editing

#7 by Joerg Arndt at Sun Jan 01 02:55:22 EST 2023

STATUS

proposed

reviewed

#6 by Jon E. Schoenfield at Sun Jan 01 02:52:45 EST 2023

STATUS

editing

proposed

#5 by Jon E. Schoenfield at Sun Jan 01 02:52:36 EST 2023

NAME

Number of 8-step knight's tours on a an (n+2) X (n+2) board summed over all starting positions.

COMMENTS

Row 8 of A186851.

EXAMPLE

Some solutions for 5X55 X 5:

.. 0.. 0.. 0.. 0.. 0.... 0.. 3.. 8.. 0.. 0.... 0.. 0.. 0.. 4.. 7.... 3.. 0.. 5.. 0.. 0

.. 0.. 0.. 7.. 0.. 0.... 0.. 0.. 0.. 0.. 0.... 2.. 5.. 8.. 0.. 0.... 6.. 0.. 2.. 0.. 0

.. 0.. 0.. 2.. 5.. 0.... 2.. 0.. 4.. 7.. 0.... 0.. 0.. 3.. 6.. 0.... 0.. 4.. 7.. 0.. 1

.. 3.. 6.. 0.. 8.. 0.... 0.. 6.. 0.. 0.. 0.... 0.. 1.. 0.. 0.. 0.... 0.. 0.. 0.. 0.. 0

.. 0.. 1.. 4.. 0.. 0.... 0.. 1.. 0.. 5.. 0.... 0.. 0.. 0.. 0.. 0.... 0.. 8.. 0.. 0.. 0

AUTHOR

R. H. Hardin , Feb 27 2011

STATUS

approved

editing