A069396 Half the number of 3 X n binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

1, 25, 377, 4541, 48329, 476389, 4461489, 40306317, 354713977, 3060942133, 26020259201, 218626028573, 1820140085705, 15043088032837, 123602247055953, 1010793162739629, 8234370308667673, 66870924588036181

Offset

2,2

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

Formula

G.f.: x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x+1)/(4*x^2-6*x+1). - Vladeta Jovovic, Jul 02 2003

2*a(n) = 8^n+A084326(n+1) -2*A186446(n). - R. J. Mathar, May 09 2023

Mathematica

Drop[CoefficientList[Series[x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x + 1)/(4*x^2 - 6*x + 1), {x, 0, 50}], x], 2] (* G. C. Greubel, Apr 22 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x+1)/(4*x^2 -6*x+1)) \\ G. C. Greubel, Apr 22 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x+1)/(4*x^2-6*x+1))); // G. C. Greubel, Apr 22 2018

Crossrefs

Cf. 1 X n A000225, 2 X n A016269, 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: A036071 A225968 A094190 * A228216 A261485 A125482

Adjacent sequences: A069393 A069394 A069395 * A069397 A069398 A069399

Keyword

nonn

Author

R. H. Hardin, Mar 22 2002

Status

approved