A069294 Number of n X 3 binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

12, 110, 926, 7556, 60920, 488860, 3915640, 31340216, 250769592, 2006308480, 16050948896, 128409116176, 1027277763840, 8218237436320, 65745948074080, 525967738606656, 4207742397091072, 33661940724484800, 269295530702399616

Offset: 2

Author

R. H. Hardin, Mar 14 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1001
• Index entries for linear recurrences with constant coefficients, signature (12,-34,14,16).

Crossrefs

Cf. n X 2 A002450, n X 4 A069295, n X 5 A069296, n X 6 A069297, n X 7 A069298, n X 8 A069299, n X 9 A069300, n X 10 A069301, n X 11 A069302, n X 12 A069303, n X 13 A069304, n X 14 A069305, read by rows A069306-A069320.

Programs

Magma

I:=[12, 110, 926, 7556]; [n le 4 select I[n] else 12*Self(n-1) - 34*Self(n-2) +14*Self(n-3) + 16*Self(n-4): n in [1..30]]; // G. C. Greubel, Apr 22 2018

Mathematica

LinearRecurrence[{12, -34, 14, 16}, {12, 110, 926, 7556}, 50] (* G. C. Greubel, Apr 22 2018 *)

PARI

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 16,14,-34,12]^(n-2)*[12;110;926;7556])[1,1] \\ Charles R Greathouse IV, May 10 2016

PARI

x='x+O('x^30); Vec(2*x^2*(6-17*x+7*x^2+8*x^3)/((1-8*x)*(2*x^3 +2*x^2-4*x+1))) \\ G. C. Greubel, Apr 22 2018

Formula

G.f.: 2*x^2*(6-17*x+7*x^2+8*x^3)/(1-8*x)/(2*x^3+2*x^2-4*x+1). - Vladeta Jovovic, Jul 02 2003