A054418 - OEIS

%I #18 Sep 08 2022 08:45:01

%S 1,8,53,352,2345,15624,104093,693504,4620369,30782536,205084165,

%T 1366343392,9103063929,60647838152,404057392237,2691973550848,

%U 17934881869985,119488539398536,796074997934037,5303733776692576

%N Number of connected 3 X n binary matrices with rightmost column [1,1,1]', divided by 4.

%C A connected (0,1) matrix is one where you can get from any black square, i.e. a 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="/A054418/b054418.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec">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.: x*(1+x)/(1-7*x+3*x^2-5*x^3). [Colin Barker, Mar 08 2012]

%t CoefficientList[Series[(1+x)/(1-7*x+3*x^2-5*x^3),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 28 2012 *)

%o (Magma) I:=[1, 8, 53]; [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_, Apr 28 2012

%Y Cf. A054417-A054421.

%K nonn,easy

%O 1,2

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

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