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A163029 Number of n X 3 binary arrays with all 1's connected and a path of 1's from top row to bottom row. 8
6, 28, 144, 730, 3692, 18666, 94384, 477264, 2413346, 12203374, 61707810, 312032874, 1577831334, 7978491800, 40344192708, 204005208738, 1031576601204, 5216289773894, 26376789637884, 133377373911160, 674438554337506 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..100

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

a(n) = 7*a(n-1) - 11*a(n-2) + 6*a(n-3) + a(n-4) - 7*a(n-5) + a(n-6). [Conjectured by R. J. Mathar, Aug 11 2009]

Proof from Peter Kagey, May 08 2019: Scanning from top to bottom, there are 6 possible intermediate states that the bottom row can be in. The transitions between these states define a 6 X 6 transition matrix whose characteristic polynomial agrees with the characteristic polynomial of the above recurrence. QED

For an alternative proof see the Goodman-Strauss links. - N. J. A. Sloane, May 22 2020

CROSSREFS

Cf. A001333 ((n-1) X 2 arrays).

Cf. also A163030, A163031, A163032, A163033, A163034, A163035, A163036.

Sequence in context: A216383 A283094 A110047 * A309490 A045722 A047129

Adjacent sequences:  A163026 A163027 A163028 * A163030 A163031 A163032

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 20 2009

STATUS

approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)