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Search: id:A116470
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| A116470 |
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All distinct Fibonacci and Lucas numbers. |
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+0
3
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| 0, 1, 2, 3, 4, 5, 7, 8, 11, 13, 18, 21, 29, 34, 47, 55, 76, 89, 123, 144, 199, 233, 322, 377, 521, 610, 843, 987, 1364, 1597, 2207, 2584, 3571, 4181, 5778, 6765, 9349, 10946, 15127, 17711, 24476, 28657, 39603, 46368, 64079, 75025, 103682, 121393, 167761
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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See A115339 for an essentially identical sequence.
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FORMULA
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a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5, a(6) = 7, a(n) = a(n-2) + a(n-4) for n>6. a(2n) = Lucas[n+1] = Fibonacci[n] + Fibonacci[n+2] for n>1. a(2n+1) = Fibonacci[n+3] for n>2.
G.f.:-x*(x^2+x+1)*(x^3+x+1)/(-1+x^4+x^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
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CROSSREFS
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Union of A000045 and A000032.
Sequence in context: A031121 A080655 A118083 this_sequence A115649 A111795 A046098
Adjacent sequences: A116467 A116468 A116469 this_sequence A116471 A116472 A116473
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 13 2006
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