cp's OEIS Frontend

A379393 Maximum number of connections for a 3 X n rectangle.

%I A379393 #13 Dec 23 2024 01:58:15
%S A379393 1,6,72,277,1910,8657,27442,97132,295752,967914,2922814
%N A379393 Maximum number of connections for a 3 X n rectangle.
%C A379393 In a 3 X n board (with n > 1) with numbers 1, 2 and 3, at least 2 of each, find the arrangement with more solutions connecting a pair of numbers 1 and a pair of number 2 and a pair of number 3, covering the entire board and without passing through the same square twice.
%C A379393 Terms a(5) and a(7)-a(12) from Giorgio Vecchi.
%H A379393 Rodolfo Kurchan and Claudio Meller, <a href="https://www.puzzlefun.online/problems">Number Connections</a>, Puzzle Fun, Problems (2024).
%e A379393 For n = 2 with the board
%e A379393   +---+---+
%e A379393   | 1 | 1 |
%e A379393   +---+---+
%e A379393   | 2 | 2 |
%e A379393   +---+---+
%e A379393   | 3 | 3 |
%e A379393   +---+---+
%e A379393 There is only 1 solution being the squares with these letters:
%e A379393   +---+---+
%e A379393   | A | B |
%e A379393   +---+---+
%e A379393   | C | D |
%e A379393   +---+---+
%e A379393   | E | F |
%e A379393   +---+---+
%e A379393 Solution:
%e A379393 1) AB - CD - EF
%e A379393 There is one solution so a(2) = 1.
%e A379393 .
%e A379393 For n = 3 with the board
%e A379393   +---+---+---+
%e A379393   | 1 | 3 | 3 |
%e A379393   +---+---+---+
%e A379393   | 1 | 2 | 2 |
%e A379393   +---+---+---+
%e A379393   | 1 | 2 | 2 |
%e A379393   +---+---+---+
%e A379393 the maximum number of solutions is 6 being the squares with this letters:
%e A379393   +---+---+---+
%e A379393   | A | B | C |
%e A379393   +---+---+---+
%e A379393   | D | E | F |
%e A379393   +---+---+---+
%e A379393   | G | H | I |
%e A379393   +---+---+---+
%e A379393 Solutions:
%e A379393   1) ADG - BC - HEFI
%e A379393   2) ADG - BC - FEHI
%e A379393   3) ADG - BC - EFIH
%e A379393   4) ADG - BC - EHIF
%e A379393   5) ADG - BEFC - HI
%e A379393   6) ADEHG - BC - FI
%e A379393 There are six solutions so a(3) = 6.
%Y A379393 Cf. A379241.
%K A379393 nonn,more
%O A379393 2,2
%A A379393 _Rodolfo Kurchan_, Dec 22 2024