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A194021 Number of ways to arrange 4 points on an n X n X n triangular grid on an isosceles triangle so that it balances at the midpoint of its central altitude. 1

%I #14 May 05 2018 04:20:58

%S 0,0,1,8,26,75,182,387,756,1382,2379,3915,6198,9486,14110,20475,29054,

%T 40437,55309,74466,98850,129548,167784,214986,272758,342900,427453,

%U 528698,649148,791631,959254,1155429,1383930,1648890,1954791,2306565

%N Number of ways to arrange 4 points on an n X n X n triangular grid on an isosceles triangle so that it balances at the midpoint of its central altitude.

%C Column 4 of A194024.

%H R. H. Hardin, <a href="/A194021/b194021.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-4) + 5*a(n-6) - 3*a(n-7) + 3*a(n-8) - 5*a(n-9) + 2*a(n-11) + 2*a(n-13) - 3*a(n-14) + a(n-15).

%F Empirical g.f.: x^3*(1 + 5*x + 4*x^2 + 13*x^3 + 11*x^4 + 7*x^5 + 6*x^6 + x^7) / ((1 - x)^7*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - _Colin Barker_, May 05 2018

%e Some solutions for 5 X 5 X 5:

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

%e .....0.0........0.0........1.0........0.0........1.1........1.1........0.1

%e ....0.1.1......1.0.0......0.0.0......1.1.0......0.0.1......0.0.0......1.1.0

%e ...0.0.0.0....0.1.0.1....0.1.0.0....0.0.0.0....0.0.0.0....0.1.1.0....0.0.1.0

%e ..0.1.0.0.0..0.0.0.0.0..0.0.0.1.0..0.0.0.1.0..0.1.0.0.0..0.0.0.0.0..0.0.0.0.0

%Y Cf. A194024.

%K nonn

%O 1,4

%A _R. H. Hardin_, Aug 12 2011

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)