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 A239032 Number of 5 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3. 1

%I #8 Oct 25 2018 08:13:27

%S 4,16,54,149,354,757,1495,2773,4888,8258,13456,21249,32642,48927,

%T 71737,103105,145528,202036,276266,372541,495954,652457,848955,

%U 1093405,1394920,1763878,2212036,2752649,3400594,4172499,5086877,6164265,7427368,8901208

%N Number of 5 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.

%H R. H. Hardin, <a href="/A239032/b239032.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/144)*n^6 - (17/240)*n^5 + (169/144)*n^4 - (81/16)*n^3 + (1463/72)*n^2 - (1001/30)*n + 25 for n>1.

%F Conjectures from _Colin Barker_, Oct 25 2018: (Start)

%F G.f.: x*(4 - 12*x + 26*x^2 - 33*x^3 + 25*x^4 - 6*x^5 - 3*x^6 + 4*x^7) / (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>8.

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

%Y Row 5 of A239030.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 09 2014

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Last modified May 31 16:17 EDT 2023. Contains 363068 sequences. (Running on oeis4.)