The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A188150 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A188150

Number of 5-step self-avoiding walks on an n X n square summed over all starting positions.
(history; published version)

#14 by Susanna Cuyler at Fri Apr 27 09:22:26 EDT 2018

STATUS

reviewed

approved

#13 by Michel Marcus at Fri Apr 27 05:59:49 EDT 2018

STATUS

proposed

reviewed

#12 by Jon E. Schoenfield at Fri Apr 27 05:54:58 EDT 2018

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Fri Apr 27 05:54:53 EDT 2018

EXAMPLE

.. 5.. 4.. 3.... 1.. 0.. 5.... 5.. 0.. 1.... 2.. 1.. 0.... 0.. 1.. 0.... 1.. 0.. 0.... 5.. 0.. 0

.. 0.. 1.. 2.... 2.. 3.. 4.... 4.. 3.. 2.... 3.. 4.. 5.... 0.. 2.. 3.... 2.. 0.. 0.... 4.. 3.. 0

.. 0.. 0.. 0.... 0.. 0.. 0.... 0.. 0.. 0.... 0.. 0.. 0.... 0.. 5.. 4.... 3.. 4.. 5.... 1.. 2.. 0

STATUS

reviewed

editing

#10 by Michel Marcus at Fri Apr 27 05:27:55 EDT 2018

STATUS

proposed

reviewed

#9 by Colin Barker at Fri Apr 27 05:24:46 EDT 2018

STATUS

editing

proposed

#8 by Colin Barker at Fri Apr 27 05:24:08 EDT 2018

NAME

Number of 5-step self-avoiding walks on an n X n square summed over all starting positions.

COMMENTS

Row 5 of A188147.

FORMULA

Empirical: a(n) = 100*n^2 - 360*n + 272 for n>3.

Conjectures from Colin Barker, Apr 27 2018: (Start)

G.f.: 4*x^3*(26 + 30*x - 3*x^2 - 3*x^3) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)

EXAMPLE

Some solutions for 3X33 X 3:

CROSSREFS

Cf. A188147.

AUTHOR

R. H. Hardin , Mar 22 2011

STATUS

approved

editing

#7 by N. J. A. Sloane at Mon Apr 04 16:14:07 EDT 2016

NAME

Number of 5-step self-avoiding walks on a an n X n square summed over all starting positions

Discussion

Mon Apr 04

16:14

OEIS Server: https://oeis.org/edit/global/2492

#6 by Charles R Greathouse IV at Fri Dec 18 18:17:36 EST 2015

NAME

Number of 5-step self-avoiding walks on a nXn n X n square summed over all starting positions

Discussion

Fri Dec 18

18:17

OEIS Server: https://oeis.org/edit/global/2478

#5 by Russ Cox at Sat Mar 31 12:36:11 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Mar 22 2011

Discussion

Sat Mar 31

12:36

OEIS Server: https://oeis.org/edit/global/875