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 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).

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) 153-172.

EXAMPLE

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

CROSSREFS

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 b-file to n=250 from Scott Reynolds, Mar 30 2012

STATUS

approved