



1, 64, 127, 1057, 1090, 1156, 1288, 1519, 1552, 1783, 1915, 1981, 2014, 4369, 4642, 5188, 6007, 6280, 7099, 7645, 7918, 16963, 17029, 17161, 17542, 17545, 17674, 17938, 18529, 18577, 18700, 18706, 18964, 19492, 20335, 20641, 20674, 20770, 21016, 21028, 21544, 22447, 22600, 23479, 23503, 23995, 24187, 24253, 24286, 24865, 24898, 24964
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 1bit 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 0bits and 1bits (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



PROG



CROSSREFS

Cf. A258002 (a subsequence; terms that have more ones than zeros in their binary representation).


KEYWORD

nonn,base


AUTHOR



STATUS

approved



