A300421 Number of n X 2 0..1 arrays with every element equal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 3, 10, 30, 96, 307, 981, 3137, 10034, 32096, 102669, 328423, 1050581, 3360673, 10750367, 34389071, 110006322, 351896433, 1125672593, 3600885592, 11518781894, 36847140260, 117869385707, 377049398986, 1206133793206, 3858270908444

Offset

1,2

Comments

Column 2 of A300427.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 3*a(n-4) - 2*a(n-5) - a(n-6) for n > 7.

Empirical g.f.: -x*(-x^6+x^4+3*x^3-1)/(x^6+2*x^5+3*x^4-x^2-3*x+1). - Simon Plouffe, Jun 20 2018

Example

Some solutions for n=5:
  0 1   0 1   0 0   0 0   0 1   0 0   0 0   0 0   0 1   0 0
  0 1   0 1   0 1   1 1   0 1   0 1   1 0   1 1   0 1   0 0
  0 0   1 0   0 1   1 1   0 0   1 0   1 1   0 0   1 0   1 1
  1 1   0 1   1 0   0 1   0 1   0 1   0 0   0 0   1 0   0 1
  0 0   1 1   0 0   0 0   0 1   1 1   1 1   1 1   1 1   0 0

Crossrefs

Cf. A300427.

Sequence in context: A033113 A360714 A290718 * A302289 A003441 A136841

Adjacent sequences: A300418 A300419 A300420 * A300422 A300423 A300424

Keyword

nonn

Author

R. H. Hardin, Mar 05 2018

Status

approved