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Search: id:A126116
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| A126116 |
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a(0) to a(3)=1; a(n+4) = a(n+3) + a(n+1) + a(n). |
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+0
1
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| 1, 1, 1, 1, 3, 5, 7, 11, 19, 31, 49, 79, 129, 209, 337, 545, 883, 1429, 2311, 3739, 6051, 9791, 15841, 25631, 41473, 67105, 108577, 175681, 284259, 459941, 744199, 1204139, 1948339, 3152479, 5100817, 8253295, 13354113, 21607409, 34961521
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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This sequence has the same growth rate as the Fibonacci sequence, since x^4-x^3-x-1 has the real roots phi and -1/phi.
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REFERENCES
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Wolfram, S., A New Kind of Science. Champaign, IL: Wolfram Media, pp. 82-92, 2002
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LINKS
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Kelley L. Ross, The Golden Ratio and The Fibonacci Numbers
Eric Weisstein's World of Mathematics, MathWorld: Golden Ratio
Wikipedia, Golden Ratio
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CROSSREFS
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Cf. Fibonacci numbers A000045; Lucas numbers A000032; Tribonacci numbers A000213; Tetranacci numbers A000288; Pentanacci numbers A000322; Hexanacci numbers A000383; 7th order Fibonacci numbers A060455; Octanacci numbers A079262; 9th order Fibonacci sequence A127193; 10th order Fibonacci sequence A127194; 11th order Fibonacci sequence A127624, A128429.
Sequence in context: A137814 A161423 A077858 this_sequence A133846 A060643 A025077
Adjacent sequences: A126113 A126114 A126115 this_sequence A126117 A126118 A126119
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KEYWORD
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nonn
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AUTHOR
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Luis A Restrepo (luisiii(AT)mac.com), Mar 05 2007
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Mar 09 2007
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