|
%I #30 Mar 29 2023 15:33:20
%S 9,65,201,449,841,1409,2185,3201,4489,6081,8009,10305,13001,16129,
%T 19721,23809,28425,33601,39369,45761,52809,60545,69001,78209,88201,
%U 99009,110665,123201,136649,151041,166409,182785,200201,218689,238281,259009,280905,304001
%N a(n) = (16/3)*(n+1)*n*(n-1) + 8*n^2 + 1.
%C 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, 32*n^5).
%H Colin Barker, <a href="/A212668/b212668.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_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 2/(2*n+1)*Sum_{i=1..n} tan^5(Pi*i/(2*n+1)) * sin(2*Pi*i/(2*n+1)).
%F G.f.: x*(9+29*x-5*x^2-x^3) / (1-x)^4. - _Colin Barker_, Nov 30 2015
%t LinearRecurrence[{4, -6, 4, -1}, {9, 65, 201, 449}, 40] (* _Vincenzo Librandi_, Dec 01 2015 *)
%t CoefficientList[Series[x (9+29x-5x^2-x^3)/(1-x)^4,{x,0,40}],x] (* _Harvey P. Dale_, Mar 29 2023 *)
%o (PARI) a(n)=16*(n+1)*n*(n-1)/3+8*n^2+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (PARI) Vec(x*(9+29*x-5*x^2-x^3)/(1-x)^4 + O(x^100)) \\ _Colin Barker_, Nov 30 2015
%o (Magma) [(16/3)*(n+1)*n*(n-1)+8*n^2+1: n in [1..40]]; // _Vincenzo Librandi_, Dec 01 2015
%Y Cf. A038754, A084990, A091042, A212500, A212592.
%K nonn,easy
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, May 23 2012
|
