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A116513
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Number of distinct hexagons of n points chosen from triangular lattice A_2 with sides parallel to the principal axes of that lattice. Degenerate sides (of length 1) are permitted.
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3
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1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 3, 5, 4, 5, 6, 5, 4, 7, 6, 6, 7, 6, 6, 9, 7, 7, 8, 8, 8, 10, 6, 8, 11, 10, 9, 12, 7, 10, 12, 10, 8, 13, 11, 12, 13, 10, 10, 15, 12, 13, 12, 12, 12, 18, 11, 13, 15, 12, 14, 18, 13, 14, 18
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OFFSET
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1,3
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COMMENTS
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This sequence is to the lattice A2 as sequence A038548 is to the lattice D2; presumably other lattices have analogous sequences.
a(n) is also the number of 4-tuples (p,b,c,d) of nonnegative integers satisfying b <= c <= d, b + c + d < p, and n = t(p) - t(b) - t(c) - t(d) where t(x) is the x-th triangular number (A000217).
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LINKS
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EXAMPLE
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a(7) = 3 because (reading the rows of the hexagons) 7 = 3+4 = 2+3+2.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms up to n=68. and b-file to n=250 from Scott Reynolds, Mar 30 2012
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STATUS
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approved
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