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.

A330610 Number of near-magic (only short lines are magic) knight's tours on a 4 X 2n board.

This page as a plain text file.
%I A330610 #10 Jan 14 2020 01:02:52
%S A330610 0,0,0,4,16,72,244,1012,3976,18440,81252,388188,1800728,8769964
%N A330610 Number of near-magic (only short lines are magic) knight's tours on a 4 X 2n board.
%C A330610 A semi-magic knight's tour is a tour that adds to a constant sum in every line in one direction, but not in every line in the perpendicular direction. A near-magic tour is a special type of semi-magic tour in which the non-magic direction has the lines add to the magic constant and two other values. Such tours are of interest on boards where magic tours don't exist.
%H A330610 G. P. Jelliss, <a href="https://www.mayhematics.com/t/mk.htm">Semi-Magic Knight's Tours</a>.
%H A330610 Awani Kumar, <a href="https://arxiv.org/abs/1802.09340">Studies in Tours of Knight on Rectangular Boards</a>, arXiv:1802.09340 [math.GM], 2018.
%e A330610 Example of 4 X 14 near-magic knight's tour. All short lines add to 114 and the long lines add to the magic constant 399 and 399 +- 4.
%e A330610    1 54 25 32  5 36 23 50 19 44  9 40 15 46
%e A330610   28 31  4 53 24 51 20 35  8 39 14 45 10 41
%e A330610   55  2 29 26 33  6 37 22 49 18 43 12 47 16
%e A330610   30 27 56  3 52 21 34  7 38 13 48 17 42 11
%Y A330610 Cf. A328816, A329483.
%K A330610 nonn,hard,more
%O A330610 1,4
%A A330610 _Awani Kumar_, Dec 20 2019