A252718 Number of (n+2) X (7+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

237, 107, 114, 153, 211, 270, 373, 522, 672, 938, 1322, 1704, 2388, 3379, 4354, 6113, 8673, 11166, 15693, 22312, 28696, 40358, 57486, 73856, 103928, 148285, 190314, 267933, 382891, 490926, 691453, 989592, 1267608, 1786118, 2559836, 3276048

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-3) - 11*a(n-6) + 5*a(n-9) + 2*a(n-12) - a(n-15) for n>17.

Empirical g.f.: x*(237 + 107*x + 114*x^2 - 1269*x^3 - 431*x^4 - 414*x^5 + 2062*x^6 + 433*x^7 + 306*x^8 - 802*x^9 - 24*x^10 + 72*x^11 - 376*x^12 - 80*x^13 - 56*x^14 + 169*x^15 + 16*x^16) / ((1 - x)*(1 + x + x^2)*(1 - 3*x^3 + x^6)*(1 - 2*x^3 - x^6)). - Colin Barker, Dec 05 2018

Example

Some solutions for n=4:
..0..0..1..0..0..2..0..0..2....0..1..0..0..1..0..0..1..0
..2..0..0..1..0..0..2..0..0....1..1..2..1..1..3..1..1..3
..3..0..3..3..0..3..3..0..3....3..1..1..2..1..1..3..1..1
..0..0..2..0..0..1..0..0..2....0..1..0..0..1..0..0..1..0
..1..0..0..2..0..0..1..0..0....1..1..3..1..1..2..1..1..3
..3..0..3..3..0..3..3..0..3....2..1..1..3..1..1..2..1..1

Crossrefs

Column 7 of A252719.

Sequence in context: A233200 A233221 A265372 * A036270 A217030 A048454

Adjacent sequences: A252715 A252716 A252717 * A252719 A252720 A252721

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved