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Search: id:A116591
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| A116591 |
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a(0)=1; a(n)=b(n+2)+b(n), where b(n)=A005229(n) is the sequence defined by b(1)=b(2)=1, b(n)=b(b(n-2))+b(n-b(n-2)) for n>2. |
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+0
1
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| 1, 3, 4, 5, 7, 8, 10, 11, 13, 13, 15, 16, 18, 19, 21, 22, 23, 25, 26, 28, 30, 31, 33, 33, 35, 36, 37, 39, 39, 41, 42, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 59, 59, 60, 61, 62, 64, 66, 68, 70, 71, 73, 73, 75, 76, 77, 79, 80, 82, 84, 85, 87, 88, 89, 90, 91, 91, 93, 94, 96, 98
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A similar definition applied to the Fibonacci sequence (A000045) leads to the Lucas sequence (A000032).
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FORMULA
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a(n)=A005229(n+2)+A005229(n) for n>=1.
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MAPLE
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b:=proc(n) option remember; if n<=2 then 1 else b(b(n-2))+b(n-b(n-2)): fi: end: seq(b(n), n=1..75): a[0]:=1: for n from 1 to 70 do a[n]:=b(n)+b(n+2) od: seq(a[n], n=0..70);
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MATHEMATICA
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M[0] = 0; M[1] = M[2] = 1; M[n_Integer?Positive] := M[n] = M[M[n - 2]] + M[n - M[n - 2]] L[0] = 1; L[n_] := L[n] = M[n - 1] + M[n + 1] a = Table[L[n], {n, 1, 200}]
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CROSSREFS
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Cf. A000030, A005185, A005229.
Sequence in context: A063732 A047367 A039043 this_sequence A136119 A110882 A089230
Adjacent sequences: A116588 A116589 A116590 this_sequence A116592 A116593 A116594
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 27 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 15 2006
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