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Search: id:A024036
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| 0, 3, 15, 63, 255, 1023, 4095, 16383, 65535, 262143, 1048575, 4194303, 16777215, 67108863, 268435455, 1073741823, 4294967295, 17179869183, 68719476735, 274877906943, 1099511627775
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OFFSET
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0,2
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COMMENT
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This sequence is the normalized length per iteration of the space-filling Peano-Hilbert curve. The curve remains in a square, but its length increases without bound. The length of the curve, after n iteration in a unit square, is a(n)*2^(-n) where a(n) = 4*a(n-1)+3. This is the sequence of a(n) values. a(n)*(2^(-n)*2^(-n)) tends to 1, area of the square where the curve is generated, as n increase. The ratio between the number of segments of the curve at n-th iteration (A015521) and a(n) tend to 4/5 as n increase. - Giorgio Balzarotti (greenblue(AT)tiscali.it), Mar 16 2006
Numbers whose base 4 representation is 333....3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 03 2007
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REFERENCES
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G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
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FORMULA
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G.f.: 3*x/(-1+x)/(-1+4*x) = 1/(-1+x)-1/(-1+4*x) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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CROSSREFS
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Equals 3 * A002450(n).
Cf. A015521.
Sequence in context: A122671 A067562 A062211 this_sequence A103454 A111303 A118339
Adjacent sequences: A024033 A024034 A024035 this_sequence A024037 A024038 A024039
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KEYWORD
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nonn
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AUTHOR
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njas
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