

A212705


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).


2



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

1,1


LINKS

Table of n, a(n) for n=1..21.
Vladimir Shevelev, On monotonic strengthening of Newmanlike phenomenon on (2m+1)multiples in base 2m, arXiv:0710.3177v2 [math.NT], 2007
Index entries for linear recurrences with constant coefficients, signature (8,28,56,70,56,28,8,1).


FORMULA

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^3868*n^2+322n45).
G.f.: 2*x*(27+1394*x+7273*x^2+7308*x^3+1373*x^4+34*x^5x^6)/(1x)^8. [Bruno Berselli, May 24 2012]


CROSSREFS

Cf. A038754, A084990, A091042, A212500, A212592, A212593, A212594, A212668, A212669, A212670.
Sequence in context: A042405 A187304 A309422 * A046199 A245831 A291071
Adjacent sequences: A212702 A212703 A212704 * A212706 A212707 A212708


KEYWORD

nonn,easy,base


AUTHOR

Vladimir Shevelev and Peter J. C. Moses, May 24 2012


STATUS

approved



