|
%I #29 Mar 29 2024 10:22:57
%S 1,6,11,106,201,2022,3843,38794,73745,744646,1415547,14293930,
%T 27172313,274381478,521590643,5266936010,10012281377,101102361990,
%U 192192442603,1940727511786,3689262580969,37253563629926,70817864678883,715107089849866
%N a(n) is the difference between multiples of 7 with even and odd digit sum in base 6 in interval [0,6^n).
%C In general for all z, given a sequence of the form: a(n) is the difference between multiples of 2z+1 with even and odd digit sum in base 2z in interval [0,(2z)^n); then a(n) = (a(n+1) + a(n-1))/2 when n is even. The equation applies here where z=3. - _Bob Selcoe_, Jun 10 2014
%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:0710.3177 [math.NT], 2007.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,21,0,-35,0,7).
%F For n>=7, a(n) = 21*a(n-2)-35*a(n-4)+7*a(n-6).
%F G.f.: x*(1+6*x-10*x^2-20*x^3+5*x^4+6*x^5)/(1-21*x^2+35*x^4-7*x^6). [_Bruno Berselli_, May 22 2012]
%F a(n) = 2a(n-1) - a(n-2) when n is odd; a(n) = (a(n+1) + a(n-1))/2 when n is even. - _Bob Selcoe_, Jun 10 2014
%t LinearRecurrence[{0, 21, 0, -35, 0, 7}, {1, 6, 11, 106, 201, 2022}, 24] (* _Bruno Berselli_, May 22 2012 *)
%Y Cf. A038754, A212500, A091042.
%K nonn,base,easy
%O 1,2
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, May 22 2012
|
