login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of slanted n X 4 (i=1..n) X (j=i..4+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
1

%I #8 Mar 26 2018 09:54:00

%S 33,94,158,243,346,467,606,763,938,1131,1342,1571,1818,2083,2366,2667,

%T 2986,3323,3678,4051,4442,4851,5278,5723,6186,6667,7166,7683,8218,

%U 8771,9342,9931,10538,11163,11806,12467,13146,13843,14558,15291,16042,16811

%N Number of slanted n X 4 (i=1..n) X (j=i..4+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.

%H R. H. Hardin, <a href="/A165378/b165378.txt">Table of n, a(n) for n=2..99</a>

%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=7.

%F Conjectures from _Colin Barker_, Mar 26 2018: (Start)

%F G.f.: x^2*(33 - 5*x - 25*x^2 + 18*x^3 - 3*x^4) / (1 - x)^3.

%F a(n) = 9*n^2 + 4*n - 2 for n>3.

%F (End)

%e Some solutions for n=4:

%e ...1.1.2.2.........1.1.2.2.........1.1.1.2.........1.1.2.2......

%e .....1.1.3.4.........1.1.4.4.........3.3.2.2.........1.1.2.2....

%e .......1.3.4.4.........1.3.4.4.........3.3.2.2.........3.3.4.4..

%e .........3.3.4.4.........3.3.4.4.........3.3.3.4.........3.3.4.4

%e ------

%e ...1.1.2.2.........1.1.2.2.........1.2.2.2.........1.1.2.2......

%e .....1.3.2.2.........3.3.2.2.........3.3.2.2.........1.3.2.2....

%e .......3.3.4.4.........3.3.4.4.........3.3.2.2.........3.3.2.3..

%e .........3.3.4.4.........3.3.4.4.........3.3.3.4.........3.3.3.4

%e ------

%e ...1.1.2.2.........1.1.2.2.........1.1.2.2.........1.3.2.2......

%e .....1.1.1.4.........1.1.2.2.........1.2.4.4.........3.3.2.2....

%e .......3.3.4.4.........1.3.4.4.........2.2.4.4.........3.3.2.3..

%e .........3.3.4.4.........3.3.4.4.........3.3.4.4.........3.3.3.4

%K nonn

%O 2,1

%A _R. H. Hardin_, Sep 17 2009