A207118 Number of n X 3 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.

6, 36, 102, 289, 612, 1296, 2340, 4225, 6890, 11236, 17066, 25921, 37352, 53824, 74472, 103041, 138030, 184900, 241230, 314721, 401676, 512656, 642252, 804609, 992082, 1223236, 1487570, 1809025, 2173520, 2611456, 3104336, 3690241, 4345302

Offset

1,1

Comments

Column 3 of A207123.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +4*a(n-2) -10*a(n-3) -5*a(n-4) +20*a(n-5) -20*a(n-7) +5*a(n-8) +10*a(n-9) -4*a(n-10) -2*a(n-11) +a(n-12).

Conjectures from Colin Barker, Feb 20 2018: (Start)

G.f.: x*(6 + 24*x + 6*x^2 + x^3 + 16*x^4 - 4*x^5 - 20*x^6 + 6*x^7 + 10*x^8 - 4*x^9 - 2*x^10 + x^11) / ((1 - x)^7*(1 + x)^5).

a(n) = (n^6 + 24*n^5 + 208*n^4 + 816*n^3 + 1600*n^2 + 1536*n + 576) / 576 for n even.

a(n) = (n^6 + 24*n^5 + 205*n^4 + 768*n^3 + 1315*n^2 + 936*n + 207) / 576 for n odd.

(End)

Example

Some solutions for n=4:
..1..1..0....1..0..1....1..1..0....1..1..1....0..0..0....0..1..1....1..1..1
..0..0..0....0..1..1....1..1..0....1..1..1....0..1..1....0..1..1....1..1..1
..0..0..0....0..0..0....1..1..0....1..1..1....0..0..0....0..1..1....0..1..1
..0..0..0....0..0..0....1..1..0....1..1..1....0..0..0....0..1..1....0..1..1

Crossrefs

Cf. A207123.

Sequence in context: A207243 A207237 A207070 * A207704 A207495 A207249

Adjacent sequences: A207115 A207116 A207117 * A207119 A207120 A207121

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved