

A116513


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.


3



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

1,3


COMMENTS

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 4tuples (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 xth triangular number (A000217).


LINKS

Scott Reynolds, Table of n, a(n) for n = 1..250
Nino Bašić, Patrick W. Fowler, Tomaž Pisanski, Stratified Enumeration of Convex Benzenoids, MATCH Commun. Math. Comput. Chem. 80 (2018) 153172.


EXAMPLE

a(7) = 3 because (reading the rows of the hexagons) 7 = 3+4 = 2+3+2.


CROSSREFS

Cf. A038548.
Sequence in context: A340542 A283303 A280079 * A122651 A343378 A300013
Adjacent sequences: A116510 A116511 A116512 * A116514 A116515 A116516


KEYWORD

nonn


AUTHOR

Allan C. Wechsler, Mar 23 2006


EXTENSIONS

More terms up to n=32 from Allan C. Wechsler, Mar 31 2006
Corrected and extended to n=36 by Allan C. Wechsler, Feb 15 2008
More terms up to n=68. and bfile to n=250 from Scott Reynolds, Mar 30 2012


STATUS

approved



