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 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. 1
 0, 1, 17, 105, 410, 1225, 3066, 6762, 13560, 25245, 44275, 73931, 118482, 183365, 275380, 402900, 576096, 807177, 1110645, 1503565, 2005850, 2640561, 3434222, 4417150, 5623800, 7093125, 8868951, 11000367, 13542130, 16555085, 20106600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Column 3 of A194480. LINKS R. H. Hardin, Table of n, a(n) for n = 1..200 FORMULA 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. Empirical g.f.: x^2*(1 + 10*x + 7*x^2 - 3*x^3) / (1 - x)^7. - Colin Barker, May 05 2018 EXAMPLE The 17 solutions for 3 X 3 X 3: .     1         1         1         1         1         1    1 1       1 0       1 0       0 1       0 1       0 0   0 0 0     0 1 0     0 0 1     1 0 0     0 1 0     1 1 0          1         1         0         0         0         0 0       0 0       1 1       1 1       1 1        1 0 1     0 1 1     1 0 0     0 1 0     0 0 1     0         0         0         0         0         0    1 0       1 0       1 0       0 1       0 1       0 1   1 1 0     1 0 1     0 1 1     1 1 0     1 0 1     0 1 1 [edited by Jon E. Schoenfield, May 05 2018] CROSSREFS Cf. A194480. Sequence in context: A329386 A095785 A194131 * A164745 A221938 A121823 Adjacent sequences:  A194472 A194473 A194474 * A194476 A194477 A194478 KEYWORD nonn AUTHOR R. H. Hardin, Aug 26 2011 STATUS approved

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Last modified September 17 16:32 EDT 2021. Contains 347487 sequences. (Running on oeis4.)