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A258205
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Number of strictly non-overlapping holeless polyhexes of perimeter 2n with bilateral symmetry, counted up to rotation.
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5
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0, 0, 1, 0, 1, 1, 3, 1, 8, 5, 20, 11, 61
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OFFSET
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1,7
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COMMENTS
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This sequence counts by perimeter length those holeless polyhexes that stay same when they are flipped over and rotated appropriately.
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.
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LINKS
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FORMULA
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Other identities and observations. For all n >= 1:
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PROG
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(Scheme)
(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)))))))
(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.
;; Code for isA258005? given in A258005.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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