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%I #10 Jul 06 2015 23:41:25
%S 0,0,1,0,1,1,3,3,16,23,80,183,563
%N Number of one-sided strictly non-overlapping holeless polyhexes of perimeter 2n, counted up to rotation.
%C For n >= 1, a(n) gives the total number of terms k in A258003 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) - A258205(n).
%F a(n) <= A258017(n).
%o (Scheme)
%o (define (A258204 n) (let loop ((k (+ 1 (expt 2 (+ n n)))) (c 0)) (cond ((pow2? k) c) (else (loop (+ 1 k) (+ c (if (isA258003? 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 isA258003? given in A258003.
%Y Cf. A057779, A258003, A258017, A258205, A258206.
%K nonn,more
%O 1,7
%A _Antti Karttunen_, May 31 2015
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