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A212706 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). 1

%I

%S 81,5825,73745,461313,1951057,6418369,17712657,42921473,94087249,

%T 190446273,361259537,6449305089,1115101521,1841932225,2941740049,

%U 4561961985,6893373521,10179012289,14724250641,20908086785,29195724113,40152508353

%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)^9).

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

%F a(n) = 2/(2*n+1) sum{i=1,...,n} tan^9(pi*i/(2*n+1)) * sin(2*pi*i/(2*n+1)).

%F a(n)=1+n/315*(4352*n^6+15232*n^5+12992*n^4-5600*n^3-5152*n^2+5488*n-2112).

%Y Cf. A038754, A084990, A091042, A212500, A212592, A212592, A212592, A212668, A212669, A212670, A212705.

%K nonn,base

%O 1,1

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

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Last modified April 18 19:33 EDT 2014. Contains 240733 sequences.