A054418 Number of connected 3 X n binary matrices with rightmost column [1,1,1]', divided by 4.

1, 8, 53, 352, 2345, 15624, 104093, 693504, 4620369, 30782536, 205084165, 1366343392, 9103063929, 60647838152, 404057392237, 2691973550848, 17934881869985, 119488539398536, 796074997934037, 5303733776692576

Offset

1,2

Comments

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.

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (7,-3,5).

Formula

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

G.f.: x*(1+x)/(1-7*x+3*x^2-5*x^3). [Colin Barker, Mar 08 2012]

Mathematica

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

Prog

(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

Crossrefs

Cf. A054417-A054421.

Sequence in context: A297334 A091870 A252824 * A293115 A337554 A370359

Adjacent sequences: A054415 A054416 A054417 * A054419 A054420 A054421

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2000

Extensions

More terms from James A. Sellers, May 23 2000

Status

approved