OFFSET
0,2
COMMENTS
These are the numbers whose binary representation traces a nonselfcrossing circuit in honeycomb lattice when its bits (from the least to the second most significant bit; the most significant 1-bit is ignored) are interpreted as directions to proceed at each vertex, with an additional condition that the final direction (angle) must be equal to the starting direction of the walk. Because each bit either adds or subtracts 60 degrees from the current phase angle, it implies that for all terms after the initial term a(1)=0 (which stands for an empty path), the difference between the number of 0-bits and 1-bits (when excluding the most significant bit which is always 1) must be either -6 or +6. And indeed, for all n >= 1, A037861(a(n)) is either 5 or -7 as A037861 takes also the most significant bit into account.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..13242 (all terms up to binary width 24+1)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, May 16 2015
STATUS
approved