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%I #8 Mar 26 2018 09:53:55
%S 105,1622,11960,63740,272548,993780,3239860,9743508,27593908,74632788,
%T 194702068,493466004,1221540916,2965389012,7081701748,16678011924,
%U 38810916532,89383135572,203992087540,461842419348,1038214750516
%N Number of slanted n X 5 (i=1..n) X (j=i..5+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="/A165374/b165374.txt">Table of n, a(n) for n=2..48</a>
%F Empirical: a(n) = 8*a(n-1) - 25*a(n-2) + 38*a(n-3) - 28*a(n-4) + 8*a(n-5) for n>=11.
%F Empirical g.f.: x^2*(105 + 782*x + 1609*x^2 + 4620*x^3 + 2932*x^4 - 3008*x^5 + 3104*x^6 + 1344*x^7 + 128*x^8) / ((1 - x)^2*(1 - 2*x)^3). - _Colin Barker_, Mar 26 2018
%e Some solutions for n=3:
%e ...1.2.2.2.2.......1.1.1.2.2.......1.1.2.2.2.......1.1.1.2.2....
%e .....3.3.3.2.2.......1.1.1.2.4.......1.3.3.2.2.......1.1.1.2.2..
%e .......3.2.2.2.4.......3.3.2.4.4.......3.3.4.4.4.......3.1.2.4.4
%e ------
%e ...1.1.2.2.2.......1.1.1.2.2.......1.1.1.1.2.......1.1.2.2.2....
%e .....1.1.1.1.1.......1.2.2.2.2.......1.1.1.2.2.......1.1.2.2.2..
%e .......3.3.3.3.4.......3.3.2.4.4.......3.3.3.4.4.......3.4.4.4.4
%e ------
%e ...1.1.2.2.2.......1.1.1.3.2.......1.1.2.2.2.......1.1.2.2.2....
%e .....1.2.3.2.4.......3.3.3.2.2.......2.2.2.4.4.......2.2.2.4.4..
%e .......3.3.3.4.4.......3.2.2.4.4.......3.4.4.4.4.......3.2.2.4.4
%K nonn
%O 2,1
%A _R. H. Hardin_, Sep 17 2009
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