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A265989
Number of n X 6 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 19 2015
STATUS
approved