A069378 Number of n X 3 binary arrays with a path of adjacent 1's from top row to bottom row.

7, 37, 197, 1041, 5503, 29089, 153769, 812849, 4296863, 22713981, 120070149, 634712209, 3355201895, 17736195433, 93756691401, 495614587553, 2619907077991, 13849295944501, 73209847696773

Offset: 1

Author

R. H. Hardin, Mar 22 2002

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Column 3 of A359576.

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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.

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(7-12*x+x^2+2*x^3-2*x^4)/(1-7*x+9*x^2+x^3-4*x^4+2*x^5))); // G. C. Greubel, Apr 22 2018

Mathematica

Rest[CoefficientList[Series[x*(7-12*x+x^2+2*x^3-2*x^4)/(1-7*x+9*x^2+x^3-4*x^4 +2*x^5), {x,0,50}], x]] (* G. C. Greubel, Apr 22 2018 *)

PARI

x='x+O('x^30); Vec(x*(7-12*x+x^2+2*x^3-2*x^4)/(1 -7*x+9*x^2 +x^3- 4*x^4+2*x^5)) \\ G. C. Greubel, Apr 22 2018

Formula

G.f.: x*(7-12*x+x^2+2*x^3-2*x^4)/(1-7*x+9*x^2+x^3-4*x^4+2*x^5). - Vladeta Jovovic, Jul 02 2003