cp's OEIS Frontend

A194475 Number of ways to arrange 3 indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.

%I A194475 #21 May 05 2018 13:34:46
%S A194475 0,1,17,105,410,1225,3066,6762,13560,25245,44275,73931,118482,183365,
%T A194475 275380,402900,576096,807177,1110645,1503565,2005850,2640561,3434222,
%U A194475 4417150,5623800,7093125,8868951,11000367,13542130,16555085,20106600
%N A194475 Number of ways to arrange 3 indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.
%C A194475 Column 3 of A194480.
%H A194475 R. H. Hardin, <a href="/A194475/b194475.txt">Table of n, a(n) for n = 1..200</a>
%F A194475 Empirical: a(n) = (1/48)*n^6 + (1/16)*n^5 - (3/16)*n^4 + (1/48)*n^3 + (1/6)*n^2 - (1/12)*n.
%F A194475 Empirical g.f.: x^2*(1 + 10*x + 7*x^2 - 3*x^3) / (1 - x)^7. - _Colin Barker_, May 05 2018
%e A194475 The 17 solutions for 3 X 3 X 3:
%e A194475 .
%e A194475     1         1         1         1         1         1
%e A194475    1 1       1 0       1 0       0 1       0 1       0 0
%e A194475   0 0 0     0 1 0     0 0 1     1 0 0     0 1 0     1 1 0
%e A194475          1         1         0         0         0
%e A194475         0 0       0 0       1 1       1 1       1 1
%e A194475        1 0 1     0 1 1     1 0 0     0 1 0     0 0 1
%e A194475     0         0         0         0         0         0
%e A194475    1 0       1 0       1 0       0 1       0 1       0 1
%e A194475   1 1 0     1 0 1     0 1 1     1 1 0     1 0 1     0 1 1
%e A194475 [edited by _Jon E. Schoenfield_, May 05 2018]
%Y A194475 Cf. A194480.
%K A194475 nonn
%O A194475 1,3
%A A194475 _R. H. Hardin_, Aug 26 2011