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A212705
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a(n) is the difference between numbers of nonnegative multiples of 2*n+1 with even and odd digit sum in base 2*n in interval [0, (2*n)^8).
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2
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54, 3220, 38794, 237832, 995710, 3256540, 8954258, 21645200, 47366982, 95758500, 181475866, 325939096, 559444366, 923676652, 1474657570, 2286163232, 3453646934, 5098701492, 7374096042, 10469422120, 14617383838
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..21.
Vladimir Shevelev, On monotonic strengthening of Newman-like phenomenon on (2m+1)-multiples in base 2m, arXiv:0710.3177v2 [math.NT], 2007
Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
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a(n) = 2/(2*n+1)*sum{i=1..n}tan^8(pi*i/(2*n+1)).
a(n) = 2/315*n*(1088*n^6+3808*n^5+3920*n^4+280*n^3-868*n^2+322n-45).
G.f.: 2*x*(27+1394*x+7273*x^2+7308*x^3+1373*x^4+34*x^5-x^6)/(1-x)^8. [Bruno Berselli, May 24 2012]
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CROSSREFS
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Cf. A038754, A084990, A091042, A212500, A212592, A212593, A212594, A212668, A212669, A212670.
Sequence in context: A189200 A042405 A187304 * A046199 A007761 A178633
Adjacent sequences: A212702 A212703 A212704 * A212706 A212707 A212708
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KEYWORD
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nonn,easy,base
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AUTHOR
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Vladimir Shevelev and Peter J. C. Moses, May 24 2012
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STATUS
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approved
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