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A163003 Number of n X 3 binary arrays with all 1s connected and a path of 1s from upper left corner to lower right corner. 2

%I #10 Jan 13 2023 14:42:15

%S 1,8,45,234,1193,6049,30616,154861,783150,3960215,20025500,101261654,

%T 512042141,2589202874,13092613725,66204360820,334770228305,

%U 1692805481383,8559872259604,43284012160451,218870755473698,1106746006355201,5596392811360844,28298825854292256

%N Number of n X 3 binary arrays with all 1s connected and a path of 1s from upper left corner to lower right corner.

%H R. H. Hardin, <a href="/A163003/b163003.txt">Table of n, a(n) for n=1..100</a>

%F From _R. J. Mathar_, Aug 11 2009: (Start)

%F Empirical: a(n) = 8*a(n-1) -17*a(n-2) +10*a(n-3) +6*a(n-4) -14*a(n-5) +7*a(n-6) +6*a(n-7) -a(n-8).

%F Empirical g.f.: -x*(1+x)*(x^4-x^3+x^2+x-1)/ ((x^2+x-1)*(x^6-7*x^5+x^4+6*x^3-11*x^2+7*x-1)). (End)

%F The above empirical formulas are correct. - _Andrew Howroyd_, Jan 06 2023

%Y Row 3 of A359573.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jul 20 2009

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