Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Feb 15 2021 23:01:19
%S 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,
%T 10,9,12,7,10,12,10,8,13,11,12,13,10,10,15,12,13,12,12,12,18,11,13,15,
%U 12,14,18,13,14,18
%N 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.
%C This sequence is to the lattice A2 as sequence A038548 is to the lattice D2; presumably other lattices have analogous sequences.
%C 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).
%H Scott Reynolds, <a href="/A116513/b116513.txt">Table of n, a(n) for n = 1..250</a>
%H Nino Bašić, Patrick W. Fowler, Tomaž Pisanski, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match80/n1/match80n1_153-172.pdf">Stratified Enumeration of Convex Benzenoids</a>, MATCH Commun. Math. Comput. Chem. 80 (2018) 153-172.
%e a(7) = 3 because (reading the rows of the hexagons) 7 = 3+4 = 2+3+2.
%Y Cf. A038548.
%K nonn
%O 1,3
%A _Allan C. Wechsler_, Mar 23 2006
%E More terms up to n=32 from _Allan C. Wechsler_, Mar 31 2006
%E Corrected and extended to n=36 by _Allan C. Wechsler_, Feb 15 2008
%E More terms up to n=68. and b-file to n=250 from _Scott Reynolds_, Mar 30 2012