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Search: id:A141435
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| A141435 |
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a(1) = 1, a(2) = 2; a(n) = a(n-a(1)) + a(n-a(2)) + a(n-a(3)) + a(n-a(4)) + ... |
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+0
1
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| 1, 2, 3, 6, 11, 20, 38, 71, 132, 247, 461, 861, 1609, 3005, 5613, 10485, 19584, 36581, 68330, 127632, 238404, 445314, 831798, 1553712, 2902170, 5420945, 10125754, 18913838, 35329048, 65990929, 123264078, 230244265, 430071949, 803328933
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Thus we get a self-reference sequence that grows exponentially. a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-6) + a(n-11) + a(n-20) + ...
A fibonacci-like sequence, even closer to the tribonacci numbers.
Lim n-> oo log (a(n))/n converges.
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EXAMPLE
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a(6) = 20 because 20 = a(5) + a(4) + a(3) = 11 + 6 + 3
a(8) = 71 because 71 = a(7) + a(6) + a(5) + a(2) = 38 + 20 + 11 + 2
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MAPLE
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A141435 := proc(n) option remember; local a, i; if n <= 3 then RETURN(n); else a :=0 ; for i from 1 to n-1 do if n-procname(i) < 1 then RETURN(a); else a := a+procname(n-procname(i)) ; fi; od; RETURN(a); fi; end: for n from 1 to 80 do printf("%d, ", A141435(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 03 2008]
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CROSSREFS
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Cf. A058265, A008937, A001590, A000213, A000073, A096436, A102575, A111129.
Sequence in context: A078042 A115792 A054177 this_sequence A096080 A143658 A005230
Adjacent sequences: A141432 A141433 A141434 this_sequence A141436 A141437 A141438
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KEYWORD
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easy,nonn
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AUTHOR
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Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 03 2008
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