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.

1, 8, 45, 234, 1193, 6049, 30616, 154861, 783150, 3960215, 20025500, 101261654, 512042141, 2589202874, 13092613725, 66204360820, 334770228305, 1692805481383, 8559872259604, 43284012160451, 218870755473698, 1106746006355201, 5596392811360844, 28298825854292256

Offset: 1

Author

R. H. Hardin, Jul 20 2009

Keywords

• nonn

Links

• R. H. Hardin, Table of n, a(n) for n=1..100

Crossrefs

Row 3 of A359573.

Formula

From R. J. Mathar, Aug 11 2009: (Start)

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).

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)

The above empirical formulas are correct. - Andrew Howroyd, Jan 06 2023