A163705 Number of nX3 binary arrays with all 1s connected, a path of 1s from left column to lower right corner, and no 1 having more than two 1s adjacent

1, 7, 28, 80, 200, 469, 1064, 2359, 5144, 11091, 23739, 50569, 107380, 227518, 481337, 1017225, 2148079, 4533560, 9564187, 20170750, 42529933, 89658336, 188985456, 398310426, 839423323, 1768945377, 3727588148, 7854637968, 16550561260

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n=1..50

Formula

Empirical: a(n)=6*a(n-1)-13*a(n-2)+11*a(n-3)+a(n-4)-9*a(n-5)+7*a(n-6)-a(n-7)-2*a(n-8)+a(n-9) for n>=12

Empirical: G.f.: -x*(1+x-x^2-8*x^3+6*x^4+3*x^5-2*x^6-4*x^7-4*x^8+2*x^9+2*x^10)/((x^2+x-1) *( x^4+2*x-1) *(x-1)^3). [From R. J. Mathar, Aug 11 2009]

Example

All solutions for n=2
...0.0.0...0.0.1...1.0.0...1.0.1...1.1.0...1.1.1...1.1.1
...1.1.1...1.1.1...1.1.1...1.1.1...0.1.1...0.0.1...1.0.1

Crossrefs

Sequence in context: A223772 A024012 A352900 * A162595 A073363 A247608

Adjacent sequences: A163702 A163703 A163704 * A163706 A163707 A163708

Keyword

nonn

Author

R. H. Hardin Aug 03 2009

Status

approved