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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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

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

CROSSREFS

Row 3 of A359573.