A212705 - OEIS

%I #17 Jun 18 2017 02:23:13

%S 54,3220,38794,237832,995710,3256540,8954258,21645200,47366982,

%T 95758500,181475866,325939096,559444366,923676652,1474657570,

%U 2286163232,3453646934,5098701492,7374096042,10469422120,14617383838

%N 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).

%H Vladimir Shevelev, <a href="http://arxiv.org/abs/0710.3177">On monotonic strengthening of Newman-like phenomenon on (2m+1)-multiples in base 2m</a>, arXiv:0710.3177v2 [math.NT], 2007

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = 2/(2*n+1)*sum{i=1..n}tan^8(pi*i/(2*n+1)).

%F a(n) = 2/315*n*(1088*n^6+3808*n^5+3920*n^4+280*n^3-868*n^2+322n-45).

%F 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]

%Y Cf. A038754, A084990, A091042, A212500, A212592, A212593, A212594, A212668, A212669, A212670.

%K nonn,easy,base

%O 1,1

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, May 24 2012