A265989 Number of n X 6 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.

2, 6, 9, 4, 26, 5, 101, 17, 401, 65, 1601, 257, 6401, 1025, 25601, 4097, 102401, 16385, 409601, 65537, 1638401, 262145, 6553601, 1048577, 26214401, 4194305, 104857601, 16777217, 419430401, 67108865, 1677721601, 268435457, 6710886401, 1073741825

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Jan 09 2019: (Start)

G.f.: x*(2 + 4*x - 5*x^2 - 21*x^3 + 10*x^4 - x^5 + 8*x^6) / ((1 - x)*(1 - 2*x)*(1 + 2*x)).

a(n) = (64 - 23*(-2)^n + 27*2^n) / 64 for n>4.

(End)

Example

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

Crossrefs

Column 6 of A265991.

Sequence in context: A183000 A170821 A096667 * A225847 A021375 A190407

Adjacent sequences: A265986 A265987 A265988 * A265990 A265991 A265992

Keyword

nonn

Author

R. H. Hardin, Dec 19 2015

Status

approved