cp's OEIS Frontend

A046995 Number of Greek-key tours on a 4 X n board; i.e., self-avoiding walks on 4 X n grid starting in top left corner.

%I A046995 #28 Dec 21 2024 14:17:17
%S A046995 1,4,17,52,160,469,1337,3750,10347,28249,76382,204996,546651,1449952,
%T A046995 3828232,10067585,26384939,68941126,179658343,467084601,1211812016,
%U A046995 3138075544,8112667259,20941558268,53983767498,138989629481,357450757247,918350963486,2357213935865,6045360575469
%N A046995 Number of Greek-key tours on a 4 X n board; i.e., self-avoiding walks on 4 X n grid starting in top left corner.
%D A046995 Posting by Thomas Womack (mert0236(AT)sable.ox.ac.uk) to sci.math newsgroup, Apr 21 1999.
%H A046995 Andrew Howroyd, <a href="/A046995/b046995.txt">Table of n, a(n) for n = 1..500</a>
%H A046995 Jay Pantone, Alexander R. Klotz, and Everett Sullivan, <a href="https://arxiv.org/abs/2407.18205">Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height</a>, arXiv:2407.18205 [math.CO], 2024. See pp. 26, 30.
%H A046995 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-9,-6,5,1,-3,1).
%F A046995 a(n) = 3a(n-1)+3a(n-2)-9a(n-3)-6a(n-4)+5a(n-5)+a(n-6)-3a(n-7)+a(n-8) for n>=10. [conjectured by _Dean Hickerson_, Apr 05 2003; proved by _Jay Pantone_, Klotz, and Sullivan, Aug 01 2024]
%F A046995 G.f.: x*(-(x-1)*(x^7-x^6-2*x^5+3*x^4-2*x^3-4*x^2-2*x-1))/((x^4-2*x^3+2*x^2+2*x-1)*(x^4-x^3-3*x^2-x+1)). [conjectured by Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009; proved by _Jay Pantone_, Klotz, and Sullivan, Aug 01 2024]
%Y A046995 Row 4 of A378938.
%Y A046995 Cf. A046994.
%K A046995 nonn,easy,walk
%O A046995 1,2
%A A046995 Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr)
%E A046995 More terms from _Hugo van der Sanden_, Apr 02 2003
%E A046995 a(26) onwards from _Andrew Howroyd_, Dec 21 2024