A163030 Number of nX4 binary arrays with all 1s connected and a path of 1s from top row to bottom row.
10, 88, 920, 9362, 94280, 947760, 9528128, 95797726, 963186740, 9684246062, 97369020768, 978984263266, 9843070964036, 98965887676178, 995039757124590, 10004498940354450, 100588944638377056, 1011358574138112578
Offset: 1
Keywords
Links
- R. H. Hardin, Table of n, a(n) for n=1..44
- Chaim Goodman-Strauss, Notes on the number of m × n binary arrays with all 1’s connected and a path of 1’s from top row to bottom row (May 21 2020)
- Chaim Goodman-Strauss, Mma notebook to accompany the above document
Formula
Empirical: a(n)= 15*a(n-1) -59*a(n-2) +97*a(n-3) -19*a(n-4) -210*a(n-5) +222*a(n-6) +22*a(n-7) -113*a(n-8) +7*a(n-9) -71*a(n-10) +13*a(n-11) +a(n-12). [From R. J. Mathar, Aug 11 2009]
For a proof see the Goodman-Strauss links. - N. J. A. Sloane, May 22 2020