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.

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (13,-48,40,-8).

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

Adjacent sequences: A069414 A069415 A069416 * A069418 A069419 A069420

Keyword

nonn,easy

Author

R. H. Hardin, Mar 22 2002

Extensions

Terms a(12) and beyond from Andrew Howroyd, Oct 27 2020

Status

approved