A054419 - OEIS

%I #17 Sep 08 2022 08:45:01

%S 3,21,143,953,6347,42285,281719,1876913,12504659,83310469,555043871,

%T 3697898985,24636713627,164138517789,1093548978567,7285610864737,

%U 48539321706403,323386164243445,2154513238908591,14354130788161817

%N Number of connected 3 X n binary matrices (divided by 2).

%C A connected (0,1) matrix is one where you can get from any black square, i.e. 1, to any other by chess king moves.

%D R. Levy and J. Shapiro, Uniqueness in paint-by-numbers puzzles, preprint, 2000.

%H Vincenzo Librandi, <a href="/A054419/b054419.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -3, 5).

%F a(n) = 7*a(n-1)-3*a(n-2)+5*a(n-3).

%F G.f.: (-5*x^2-3)/(5*x^3-3*x^2+7*x-1). - _Harvey P. Dale_, Nov 23 2011

%t LinearRecurrence[{7,-3,5},{3,21,143},40] (* _Harvey P. Dale_, Nov 23 2011 *)

%o (Magma) I:=[3, 21, 143]; [n le 3 select I[n] else 7*Self(n-1)-3*Self(n-2)+5*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Feb 14 2012

%Y Cf. A054417-A054421.

%Y Number of connected 3 X n binary matrices = 2*A054419 = 4*A054417 + 2*A054418.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, May 22 2000

%E More terms from _James A. Sellers_, May 23 2000