cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A258205 Number of strictly non-overlapping holeless polyhexes of perimeter 2n with bilateral symmetry, counted up to rotation.

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%I A258205 #16 Jul 06 2015 23:41:44
%S A258205 0,0,1,0,1,1,3,1,8,5,20,11,61
%N A258205 Number of strictly non-overlapping holeless polyhexes of perimeter 2n with bilateral symmetry, counted up to rotation.
%C A258205 This sequence counts by perimeter length those holeless polyhexes that stay same when they are flipped over and rotated appropriately.
%C A258205 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 A258205 Other identities and observations. For all n >= 1:
%F A258205 a(n) = 2*A258206(n) - A258204(n).
%F A258205 a(n) <= A258018(n).
%o A258205 (Scheme)
%o A258205 (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 A258205 (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 A258205 ;; Code for isA258005? given in A258005.
%Y A258205 Cf. A057779, A258005, A258018, A258204, A258206.
%K A258205 nonn,more
%O A258205 1,7
%A A258205 _Antti Karttunen_, May 31 2015