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

1,2

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.

Sequence in context: A201190 A297089 A032208 * A368576 A055422 A204618

Adjacent sequences: A163000 A163001 A163002 * A163004 A163005 A163006

Keyword

nonn

Author

R. H. Hardin, Jul 20 2009

Status

approved