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

2,1

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).

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

Mathematica

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

Prog

(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
(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

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.

Sequence in context: A037581 A177071 A081183 * A000559 A037714 A037616

Adjacent sequences: A069291 A069292 A069293 * A069295 A069296 A069297

Keyword

nonn,easy

Author

R. H. Hardin, Mar 14 2002

Status

approved