

A258206


Number of strictly nonoverlapping holeless polyhexes of perimeter 2n, counted up to rotations and turning over.


15



0, 0, 1, 0, 1, 1, 3, 2, 12, 14, 50, 97, 312, 744, 2291
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OFFSET

1,7


COMMENTS

Differs from A057779 for the first time at n=12 as here a(12) = 97, one less than A057779(12) because this sequence excludes polyhexes with holes, the smallest which contains six hexagons in a ring, enclosing a hole of one hex, having thus perimeter of 18+6 = 24 (= 2*12) edges.
Differs from A258019 for the first time at n=13 as here a(13) = 312, one less than A258019(13) because this sequence counts only strictly nonoverlapping and nontouching polyhexpatterns, while A258019(13) already includes one specimen of helicenelike selfreaching structures.
If one counts these structures by the number of hexagons (instead of perimeter length), one obtains sequence 1, 1, 3, 7, 22, 81, ... (A018190).
a(n) is also the number of 2nstep 2dimensional closed selfavoiding paths on honeycomb lattice, reduced for symmetry.  Luca Petrone, Jan 08 2016


LINKS

Table of n, a(n) for n=1..15.
Hugo Pfoertner, Illustration of polygons of perimeter <= 20.


FORMULA

a(n) = (1/2) * (A258204(n) + A258205(n)).
Other observations. For all n >= 1:
a(n) <= A057779(n).
a(n) <= A258019(n).


PROG

(Scheme) (define (A258206 n) (* (/ 1 2) (+ (A258204 n) (A258205 n))))


CROSSREFS

Cf. A000228, A057779, A018190, A258019, A258204, A258205, A316193.
Sequence in context: A195200 A098646 A129925 * A267011 A258019 A057779
Adjacent sequences: A258203 A258204 A258205 * A258207 A258208 A258209


KEYWORD

nonn,walk,more


AUTHOR

Antti Karttunen, May 31 2015


EXTENSIONS

a(14)a(15) from Luca Petrone, Jan 08 2016


STATUS

approved



