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A238807 Number of n X 3 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the sum of elements above it, modulo 3. 1

%I

%S 4,15,48,118,254,498,916,1605,2702,4395,6936,10656,15982,23456,33756,

%T 47719,66366,90929,122880,163962,216222,282046,364196,465849,590638,

%U 742695,926696,1147908,1412238,1726284,2097388,2533691,3044190,3638797

%N Number of n X 3 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the sum of elements above it, modulo 3.

%H R. H. Hardin, <a href="/A238807/b238807.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/360)*n^6 - (1/30)*n^5 + (7/9)*n^4 - (65/12)*n^3 + (11959/360)*n^2 - (1631/20)*n + 83 for n>2.

%F Conjectures from _Colin Barker_, Oct 24 2018: (Start)

%F G.f.: x*(4 - 13*x + 27*x^2 - 43*x^3 + 51*x^4 - 41*x^5 + 27*x^6 - 16*x^7 + 6*x^8) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.

%F (End)

%e Some solutions for n=5:

%e ..0..0..2....0..0..0....2..2..0....0..0..0....0..0..2....0..2..2....0..0..2

%e ..0..2..1....0..0..2....2..1..0....0..0..0....0..0..2....0..2..2....0..0..2

%e ..0..2..2....0..0..2....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0

%e ..0..0..2....2..2..0....0..0..2....0..0..0....0..0..0....0..0..0....0..2..1

%e ..2..1..0....2..2..1....0..2..1....2..2..0....2..2..0....0..0..0....2..2..1

%Y Column 3 of A238812.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 05 2014

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Last modified May 19 16:45 EDT 2022. Contains 353846 sequences. (Running on oeis4.)