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

1,2

Links

Table of n, a(n) for n=1..23.

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

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

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.

Sequence in context: A200530 A183748 A241620 * A183740 A162872 A354337

Adjacent sequences: A069420 A069421 A069422 * A069424 A069425 A069426

Keyword

nonn,easy

Author

R. H. Hardin, Mar 22 2002

Extensions

More terms from Sean A. Irvine, Aug 23 2024

Status

approved