cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A347363 Number of self-avoiding knight's paths from the lower left corner to the lower right corner of a 3 X n chessboard.

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%I A347363 #29 Dec 09 2021 01:35:20
%S A347363 1,0,2,8,32,156,871,5292,28702,154162,845532,4662014,25579463,
%T A347363 140098348,767973001,4212065280,23097682805,126643657272,694390484065,
%U A347363 3807499106946,20877386149018,114474503105178,627683328355315,3441701959286326,18871492466212538
%N A347363 Number of self-avoiding knight's paths from the lower left corner to the lower right corner of a 3 X n chessboard.
%C A347363 If we enumerate the squares in the 3 X n board like this:
%C A347363 ------------------------------------
%C A347363 | 1 | 4 | 7 | 10 | 13 | ... | 3n-2 |
%C A347363 ------------------------------------
%C A347363 | 2 | 5 | 8 | 11 | 14 | ... | 3n-1 |
%C A347363 ------------------------------------
%C A347363 | 3 | 6 | 9 | 12 | 15 | ... |  3n  |
%C A347363 ------------------------------------
%C A347363 then a(n) is the number of self-avoiding knight's paths on such a board from square 3 to square 3n.
%e A347363 For n = 4 we have exactly 8 self-avoiding paths starting at square 3 and ending at square 12:
%e A347363   3,  4,  9, 10,  5, 12;
%e A347363   3,  4,  9,  2,  7, 12;
%e A347363   3,  8,  1,  6,  7, 12;
%e A347363   3,  4, 11,  6,  7, 12;
%e A347363   3,  8,  1,  6, 11,  4,  9,  2,  7, 12;
%e A347363   3,  4, 11,  6,  7,  2,  9, 10,  5, 12;
%e A347363   3,  8,  1,  6,  7,  2,  9, 10,  5, 12;
%e A347363   3,  8,  1,  6, 11,  4,  9, 10,  5, 12;
%Y A347363 Cf. A118067, A169696, A212715.
%K A347363 nonn,walk
%O A347363 1,3
%A A347363 _Andrzej Kukla_, Aug 29 2021
%E A347363 a(8)-a(15) from _Pontus von Brömssen_, Aug 30 2021
%E A347363 Terms a(16) and beyond from _Andrew Howroyd_, Nov 19 2021