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Search: id:A116593
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| A116593 |
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a(n)=b(n+2)+b(n), where b(n)=A006046(n) is the sequence defined by b(0)=0, b(1)=1, b(n)=2b((n-1)/2)+b((n+1)/2) for n =3,5,7,..., and b(n)=3b(n/2) for n =2,4,6,.... |
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+0
1
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| 3, 6, 12, 16, 24, 30, 42, 48, 60, 66, 78, 86, 102, 114, 138, 148, 168, 174, 186, 194, 210, 222, 246, 258, 282, 294, 318, 334, 366, 390, 438, 456, 492, 498, 510, 518, 534, 546, 570, 582, 606, 618, 642, 658, 690, 714, 762, 782, 822, 834, 858, 874, 906, 930, 978
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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A similar definition applied to the Fibonacci sequence (A000045) leads to the Lucas sequence (A000032). b(n) in the definition is also the number of odd entries in the first n rows of the Pascal triangle.
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FORMULA
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b[0] := 0 b[1] := 1 b[n_?EvenQ] := b[n] = 3*b[n/2] b[n_?OddQ] := b[n] = 2*b[(n - 1)/2] + b[(n + 1)/2] a(n) = b[n-1]+b[n+1]
a(n)=A006046(n+2)+A006046(n) for n>=1.
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MAPLE
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b:=proc(n) option remember: if n = 0 then 0 elif n=1 then 1 elif n mod 2 = 0 then 3*b(n/2) else 2*b((n-1)/2)+b((n+1)/2) fi end: a:=n->b(n+2)+b(n): seq(a(n), n=0..60);
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MATHEMATICA
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b[0] := 0 b[1] := 1 b[n_?EvenQ] := b[n] = 3*b[n/2] b[n_?OddQ] := b[n] = 2*b[(n - 1)/2] + b[(n + 1)/2] L[0] = 1; L[n_] := L[n] = b[n - 1] + b[n + 1] a = Table[L[n], {n, 1, 200}]
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CROSSREFS
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Cf. A000030, A084230.
Cf. A006046.
Sequence in context: A016052 A115803 A032602 this_sequence A109735 A086538 A127563
Adjacent sequences: A116590 A116591 A116592 this_sequence A116594 A116595 A116596
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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 njas, Apr 15 2006
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