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A085005
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A Von Koch curve related to the Golden ratio.
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6
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1, 3, 4, 4, 3, 3, 4, 4, 3, 1, 0, 0, 1, 1, 0, 0, 1, 3, 4, 4, 5, 7, 10, 12, 13, 13, 14, 16, 17, 17, 16, 16, 17, 19, 20, 20, 21, 23, 26, 28, 29, 31, 34, 38, 41, 43, 44, 46, 49, 51, 52, 52, 53, 55, 56, 56, 55, 55, 56, 58, 59, 59, 60, 62, 65, 67, 68, 68, 69, 71, 72, 72, 71, 71, 72, 72, 71
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| B. Cloitre, On parity properties of certain Beatty sequences, in preparation 2004
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LINKS
| B. Cloitre, graph of A085005(n) for n=1 up to 3874
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FORMULA
| a(n)=(-1)*sum(i=1, n, sum(j=1, i, (-1)^floor(j*(1+sqrt(5))/2)))
a(n) = 2*sum(k = 1, n, sum(i = 1, k, b(i)))-n*(n+1)/2, where b(k) = floor(phi*k)-2*floor(phi*k/2)
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PROG
| (PARI) a(n)=(-1)*sum(i=1, n, sum(j=1, i, (-1)^floor(j*(1+sqrt(5))/2)))
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CROSSREFS
| Cf. A083035, A083036, A083037, A083038, A085002, A085003, A085004.
Cf. A094200, A094201.
Sequence in context: A105736 A090283 A019917 * A035004 A000916 A014241
Adjacent sequences: A085002 A085003 A085004 * A085006 A085007 A085008
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 17 2003
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