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 A195236 Number of lower triangles of a 6 X 6 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less. 1

%I #13 May 06 2018 12:18:41

%S 2097152,10322065,20729610,31374671,42029278,52683885,63338492,

%T 73993099,84647706,95302313,105956920,116611527,127266134,137920741,

%U 148575348,159229955,169884562,180539169,191193776,201848383,212502990,223157597

%N Number of lower triangles of a 6 X 6 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.

%C Row 6 of A195232.

%H R. H. Hardin, <a href="/A195236/b195236.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 10654607*n - 11243757 for n>3.

%F Conjectures from _Colin Barker_, May 06 2018: (Start)

%F G.f.: x*(2097152 + 6127761*x + 2182632*x^2 + 237516*x^3 + 9546*x^4) / (1 - x)^2.

%F a(n) = 2*a(n-1) - a(n-2) for n>5.

%F (End)

%e Some solutions for n=5 with 0 and 5:

%e ..5............5............5............0............5............0

%e ..4.4..........4.4..........4.4..........0.1..........4.4..........1.1

%e ..4.3.3........4.3.3........3.3.3........1.1.2........3.3.3........2.1.2

%e ..3.3.3.2......4.3.3.2......3.2.2.2......1.2.2.3......2.2.2.2......1.1.2.3

%e ..3.2.2.2.1....4.4.3.2.1....2.2.2.1.1....2.2.3.3.4....1.1.1.2.2....2.1.2.3.4

%e ..2.2.1.2.1.0..4.3.3.2.1.0..3.2.2.1.0.0..2.3.2.3.4.5..0.1.1.2.1.2..1.2.2.3.4.5

%Y Cf. A195232.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 13 2011

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Last modified September 23 09:36 EDT 2023. Contains 365544 sequences. (Running on oeis4.)