|
%I #8 Mar 25 2018 11:41:52
%S 37,305,1409,4569,11449,24225,45585,78729,127369,195729,288545,411065,
%T 569049,768769,1017009,1321065,1688745,2128369,2648769,3259289,
%U 3969785,4790625,5732689,6807369,8026569,9402705,10948705,12678009,14604569
%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, and 4 in the lower right corner.
%H R. H. Hardin, <a href="/A165373/b165373.txt">Table of n, a(n) for n=2..99</a>
%F Empirical: a(n) = 5*a(n-1) - 10*a(n-2) +10*a(n-3) - 5*a(n-4) + a(n-5) for n>=8.
%F Conjectures from _Colin Barker_, Mar 25 2018: (Start)
%F G.f.: x^2*(37 + 120*x + 254*x^2 + 204*x^3 - 171*x^4 + 68*x^5) / (1 - x)^5.
%F a(n) = (1107 - 1060*n + 716*n^2 - 320*n^3 + 64*n^4) / 3 for n>2.
%F (End)
%e Some solutions for n=3:
%e ...1.2.2.2.......1.1.2.2.......1.1.2.2.......1.1.2.2.......1.1.1.2....
%e .....2.3.2.2.......1.1.1.1.......4.4.4.4.......1.1.2.2.......2.2.2.4..
%e .......3.3.3.4.......3.1.1.4.......3.3.4.4.......3.3.3.4.......3.2.4.4
%e ------
%e ...1.1.2.2.......1.1.2.2.......1.1.1.2.......1.1.1.2.......1.1.1.2....
%e .....1.1.3.3.......1.2.2.2.......1.2.2.2.......4.4.4.4.......3.3.2.4..
%e .......3.3.4.4.......3.2.2.4.......3.2.4.4.......3.3.4.4.......3.2.4.4
%K nonn
%O 2,1
%A _R. H. Hardin_, Sep 17 2009
| 