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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). 2

%I

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

%T 190446273,361259537,649305089,1115101521,1841932225,2941740049,

%U 4561961985,6893373521,10179012289,14724250641,20908086785,29195724113,40152508353,54459292177,72929296897

%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 Colin Barker, <a href="/A212706/b212706.txt">Table of n, a(n) for n = 1..1000</a>

%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>, arXiv:0710.3177 [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^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).

%F 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

%t 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 *)

%o (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

%o (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

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

%K nonn,base,easy

%O 1,1

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

%E Typo in data fixed by _Colin Barker_, Dec 01 2015

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