%I #16 Jul 06 2015 23:41:44

%S 0,0,1,0,1,1,3,1,8,5,20,11,61

%N Number of strictly non-overlapping holeless polyhexes of perimeter 2n with bilateral symmetry, counted up to rotation.

%C This sequence counts by perimeter length those holeless polyhexes that stay same when they are flipped over and rotated appropriately.

%C For n >= 1, a(n) gives the total number of terms k in A258005 with binary width = 2n + 1, or equally, with A000523(k) = 2n.

%F Other identities and observations. For all n >= 1:

%F a(n) = 2*A258206(n) - A258204(n).

%F a(n) <= A258018(n).

%o (Scheme)

%o (define (A258205 n) (let loop ((k (+ 1 (expt 2 (+ n n)))) (c 0)) (cond ((pow2? k) c) (else (loop (+ 1 k) (+ c (if (isA258005? k) 1 0)))))))

%o (define (pow2? n) (let loop ((n n) (i 0)) (cond ((zero? n) #f) ((odd? n) (and (= 1 n) i)) (else (loop (/ n 2) (1+ i)))))) ;; Gives non-false only when n is a power of two.

%o ;; Code for isA258005? given in A258005.

%Y Cf. A057779, A258005, A258018, A258204, A258206.

%K nonn,more

%O 1,7

%A _Antti Karttunen_, May 31 2015