A069423 Number of n X 3 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

1, 19, 147, 907, 5149, 28159, 151331, 806463, 4280141, 22670199, 119955523, 634412111, 3354416225, 17734138519, 93751306327, 495600489243, 2619870168133, 13849199313235, 73209594712831, 386999645945759, 2045750897807901, 10814208630415211, 57165847109895879

Offset: 1

Author

R. H. Hardin, Mar 22 2002

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-41,64,-35,-13,25,-12,2).

Crossrefs

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

Formula

a(n) = A069378(n) - 2 * A069403(n). - Sean A. Irvine, Aug 23 2024

G.f.: x*(2*x^7-10*x^6+23*x^5-18*x^4-5*x^3+21*x^2-8*x-1) / ((x-1)*(x^2-3*x+1)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)). - Alois P. Heinz, Aug 23 2024

Extensions

More terms from Sean A. Irvine, Aug 23 2024