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

1,1

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

Crossrefs

Cf. A163029-A163036.

Sequence in context: A287828 A264320 A298134 * A302149 A269008 A000826

Adjacent sequences: A163027 A163028 A163029 * A163031 A163032 A163033

Keyword

nonn

Author

R. H. Hardin Jul 20 2009

Status

approved