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Search: id:A116523
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| A116523 |
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a(0)=1, a(1)=1, a(n)=17a(n/2) for n=2,4,6,..., a(n)=16a((n-1)/2)+a((n+1)/2) for n=3,5,7,.... |
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1
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| 0, 1, 17, 33, 289, 305, 561, 817, 4913, 4929, 5185, 5441, 9537, 9793, 13889, 17985, 83521, 83537, 83793, 84049, 88145, 88401, 92497, 96593, 162129, 162385, 166481, 170577, 236113, 240209, 305745, 371281, 1419857, 1419873, 1420129, 1420385
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A 17-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 17*a(n/2) else 16*a((n-1)/2)+a((n+1)/2) fi end: seq(a(n), n=0..38);
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MATHEMATICA
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b[0] := 0 b[1] := 1 b[n_?EvenQ] := b[n] = 17*b[n/2] b[n_?OddQ] := b[n] = 16*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.
Adjacent sequences: A116520 A116521 A116522 this_sequence A116524 A116525 A116526
Sequence in context: A138393 A044062 A044443 this_sequence A135637 A040272 A062054
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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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