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A229977
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Gosper island perimeter (rounded to the nearest integer) after n iterations, let starting perimeter = 1.
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1
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1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 10, 11, 12, 14, 16, 18, 20, 23, 26, 30, 34, 38, 43, 49, 56, 63, 72, 81, 92, 105, 119, 134, 152, 173, 196, 222, 252, 286, 324, 367, 416, 472, 535, 607, 688, 780, 885, 1003
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OFFSET
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0,5
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COMMENTS
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The Gosper island curve bounds the space filled by the Peano-Gosper curve. The length of Peano-Gosper curve after n iterations (rounded to the nearest integer) is A017926(n) and the total number of elements is A000420(n). See illustration in links.
The sequence expansion ratio (a(n)/a(n-1)) is 1.133893419... which is 3*A020764.
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LINKS
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FORMULA
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a(n) = round((3/sqrt(7))^n).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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