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A212706
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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)^9).
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2
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81, 5825, 73745, 461313, 1951057, 6418369, 17712657, 42921473, 94087249, 190446273, 361259537, 649305089, 1115101521, 1841932225, 2941740049, 4561961985, 6893373521, 10179012289, 14724250641, 20908086785, 29195724113, 40152508353, 54459292177, 72929296897
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OFFSET
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1,1
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..1000
V. Shevelev, On monotonic strengthening of Newman-like phenomenon on (2m+1)-multiples in base 2m, arXiv:0710.3177 [math.NT], 2007.
Index entries for 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^9(Pi*i/(2*n+1)) * sin(2*Pi*i/(2*n+1)).
a(n) = 1+n/315*(4352*n^6 + 15232*n^5 + 12992*n^4 - 5600*n^3 - 5152*n^2 + 5488*n - 2112).
G.f.: x*(81+5177*x+29413*x^2+29917*x^3+4883*x^4+171*x^5-9*x^6-x^7) / (1-x)^8. - Colin Barker, Dec 01 2015
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MATHEMATICA
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Table[1 + n/315 (4352 n^6 + 15232 n^5 + 12992 n^4 - 5600 n^3 - 5152 n^2 + 5488 n - 2112), {n, 30}] (* Vincenzo Librandi, Dec 02 2015 *)
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PROG
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(PARI) Vec(x*(81+5177*x+29413*x^2+29917*x^3+4883*x^4+171*x^5-9*x^6-x^7)/(1-x)^8 + O(x^40)) \\ Colin Barker, Dec 01 2015
(Magma) [1+n/315*(4352*n^6+15232*n^5+12992*n^4-5600*n^3- 5152*n^2+5488*n-2112): n in [1..25]]; // Vincenzo Librandi, Dec 02 2015
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CROSSREFS
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Cf. A038754, A084990, A091042, A212500, A212592, A212592, A212592, A212668, A212669, A212670, A212705.
Sequence in context: A237300 A237937 A060349 * A036354 A205887 A205199
Adjacent sequences: A212703 A212704 A212705 * A212707 A212708 A212709
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KEYWORD
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nonn,base,easy
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AUTHOR
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Vladimir Shevelev and Peter J. C. Moses, May 24 2012
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EXTENSIONS
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Typo in data fixed by Colin Barker, Dec 01 2015
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STATUS
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approved
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