A054417 Number of connected 3 X n binary matrices with rightmost column [1,0,0]'.

1, 5, 37, 249, 1657, 11037, 73533, 489905, 3263921, 21745397, 144875541, 965212201, 6430585769, 42842841485, 285434194093, 1901663763041, 12669557966433, 84409085446373, 562363243040517, 3746663234776665

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

Mathematica

CoefficientList[Series[(1-2*x+5*x^2)/(1-7*x+3*x^2-5*x^3), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 28 2012 *)
LinearRecurrence[{7, -3, 5}, {1, 5, 37}, 20] (* Harvey P. Dale, Jan 29 2014 *)

Prog

(Magma) I:=[1, 5, 37]; [n le 3 select I[n] else 7*Self(n-1)-3*Self(n-2)+5*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 28 2012

Crossrefs

Cf. A054418-A054421.

Sequence in context: A202556 A015548 A183385 * A080507 A108049 A121141

Adjacent sequences: A054414 A054415 A054416 * A054418 A054419 A054420

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2000

Extensions

More terms from James A. Sellers, May 23 2000

Status

approved