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Search: id:A116524
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| A116524 |
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a(0)=1, a(1)=1, a(n)=13a(n/2) for n=2,4,6,..., a(n)=12a((n-1)/2)+a((n+1)/2) for n=3,5,7,.... |
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+0
1
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| 0, 1, 13, 25, 169, 181, 325, 469, 2197, 2209, 2353, 2497, 4225, 4369, 6097, 7825, 28561, 28573, 28717, 28861, 30589, 30733, 32461, 34189, 54925, 55069, 56797, 58525, 79261, 80989, 101725, 122461, 371293, 371305, 371449, 371593, 373321
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A 13-divide version of A084230.
The Harborth : f(2^k)=3^k suggests that a family of sequences of the form: f(2^k)=Prime[n]^k There does indeed seem to be an infinite family of such functions.
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REFERENCES
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Harborth, H. Number of Odd Binomial Coefficients. Proc. Amer. Math. Soc. 62, 19-22, 1977
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LINKS
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Eric Weisstein's World of Mathematics, Stolarsky-Harborth Constant
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MAPLE
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a:=proc(n) if n=0 then 0 elif n=1 then 1 elif n mod 2 = 0 then 13*a(n/2) else 12*a((n-1)/2)+a((n+1)/2) fi end: seq(a(n), n=0..40);
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MATHEMATICA
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b[0] := 0 b[1] := 1 b[n_?EvenQ] := b[n] = 13*b[n/2] b[n_?OddQ] := b[n] = 12*b[(n - 1)/2] + b[(n + 1)/2] a = Table[b[n], {n, 1, 25}]
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CROSSREFS
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Cf. A006046, A077465.
Sequence in context: A032697 A125724 A005696 this_sequence A053404 A122003 A123827
Adjacent sequences: A116521 A116522 A116523 this_sequence A116525 A116526 A116527
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 15 2006
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EXTENSIONS
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Edited by njas, Apr 16 2005
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