A297945 Number of n X 2 0..1 arrays with every element equal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

1, 4, 18, 52, 174, 604, 2048, 6948, 23652, 80488, 273840, 931808, 3170824, 10789824, 36716272, 124940880, 425158448, 1446762336, 4923157280, 16752910976, 57008139808, 193991844032, 660130925440, 2246346198336, 7644046147776

Offset

1,2

Comments

Column 2 of A297951.

Links

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

Formula

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

Empirical g.f.: x*(1 + 4*x^2 - 14*x^3 + 4*x^5) / (1 - 4*x + 2*x^2 - 2*x^3 + 6*x^4 + 4*x^5). - Colin Barker, Feb 18 2018

Example

Some solutions for n=7:
  0 0   0 1   0 1   0 0   0 1   0 1   0 1   0 0   0 0   0 0
  1 1   0 1   0 1   0 0   0 1   1 0   0 1   1 1   1 0   1 1
  1 0   1 1   0 1   0 0   0 1   0 1   0 0   0 1   1 0   0 1
  0 1   0 0   0 1   0 0   0 1   0 1   1 0   0 1   0 0   1 0
  0 0   0 1   0 0   1 1   1 0   1 0   0 1   0 1   1 0   1 0
  1 0   0 1   0 1   1 0   0 1   1 0   0 1   0 1   1 0   1 0
  1 1   0 0   1 0   0 1   0 0   1 0   1 0   1 0   1 0   1 1

Crossrefs

Cf. A297951.

Sequence in context: A300876 A301486 A284607 * A320544 A020644 A182031

Adjacent sequences: A297942 A297943 A297944 * A297946 A297947 A297948

Keyword

nonn

Author

R. H. Hardin, Jan 09 2018

Status

approved