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A069417
Number of 3 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.
92
1, 15, 147, 1231, 9539, 70679, 509019, 3596367, 25070707, 173088903, 1186544331, 8090866303, 54950124515, 372067098167, 2513408596923, 16948369098159, 114128268554323, 767705581586151, 5159843165163435, 34657637020377055, 232672006452068291, 1561421588852637335
OFFSET
1,2
FORMULA
From Andrew Howroyd, Oct 27 2020: (Start)
a(n) = A069361(n) - 2*A069396(n).
a(n) = 13*a(n-1) - 48*a(n-2) + 40*a(n-3) - 8*a(n-4) for n > 4.
G.f.: x*(1 + 2*x)/((1 - 7*x + 2*x^2)*(1 - 6*x + 4*x^2)).
(End)
EXAMPLE
From Andrew Howroyd, Oct 27 2020: (Start)
Some of the a(2) = 15 arrays are:
1 0 1 0 1 0 1 1 1 0
1 1 1 0 1 1 1 1 1 1
1 0 1 1 1 1 1 1 0 1
(End)
MATHEMATICA
LinearRecurrence[{13, -48, 40, -8}, {1, 15, 147, 1231}, 25] (* Paolo Xausa, Feb 08 2024 *)
PROG
(PARI) Vec((1 + 2*x)/((1 - 7*x + 2*x^2)*(1 - 6*x + 4*x^2)) + O(x^25)) \\ Andrew Howroyd, Oct 27 2020
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: A252982 A245755 A240419 * A051272 A021414 A211847
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 22 2002
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, Oct 27 2020
STATUS
approved