cp's OEIS Frontend

A050190 T(n,5), array T as in A050186; a count of aperiodic binary words.

%I A050190 #24 Sep 08 2022 08:44:58
%S A050190 0,6,21,56,126,250,462,792,1287,2002,3000,4368,6188,8568,11628,15500,
%T A050190 20349,26334,33649,42504,53125,65780,80730,98280,118755,142500,169911,
%U A050190 201376,237336,278256,324625,376992,435897,501942
%N A050190 T(n,5), array T as in A050186; a count of aperiodic binary words.
%H A050190 G. C. Greubel, <a href="/A050190/b050190.txt">Table of n, a(n) for n = 5..1000</a>
%H A050190 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,2,-8,12,-8,2,-1,4,-6,4, -1).
%F A050190 a(n) = n * A051170(n).
%F A050190 From _Ralf Stephan_, Aug 18 2004: (Start)
%F A050190 G.f.: (x^5*(3 + x^2 + x^3)*(2 - x + 2*x^2 + x^3 + x^4))/((1 - x)^4*(1 - x^5)^2). (corrected by _G. C. Greubel_, Nov 27 2017)
%F A050190 a(n) = A000389(n) - [5 divides n]*n/5.
%F A050190 a(n) = n*floor(C(n-1, 4)/5). (End)
%F A050190 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 2*a(n-5) - 8*a(n-6) + 12*a(n-7) - 8*a(n-8) + 2*a(n-9) - a(n-10) + 4*a(n-11) - 6*a(n-12) + 4*a(n-13) - a(n-14). - _R. J. Mathar_, May 20 2013
%t A050190 Table[n*Floor[Binomial[n - 1, 4]/5], {n, 5, 50}] (* _G. C. Greubel_, Nov 25 2017 *)
%t A050190 Drop[CoefficientList[Series[(x^5*(3 + x^2 + x^3)*(2 - x + 2*x^2 + x^3 + x^4))/((1 - x)^4*(1 - x^5)^2), {x, 0, 50}], x], 4] (* _G. C. Greubel_, Nov 27 2017 *)
%o A050190 (PARI) for(n=5,40, print1(n*floor(binomial(n-1, 4)/5), ", ")) \\ _G. C. Greubel_, Nov 25 2017
%o A050190 (Magma) [n*floor(Binomial(n-1, 4)/5): n in [5..40]]; // _G. C. Greubel_, Nov 25 2017
%o A050190 (PARI) x='x+O('x^30); concat([0], Vec((x^5*(3 + x^2 + x^3)*(2 - x + 2*x^2 + x^3 + x^4))/((1 - x)^4*(1 - x^5)^2))) \\ _G. C. Greubel_, Nov 27 2017
%Y A050190 Cf. A000389, A050186.
%K A050190 nonn,easy
%O A050190 5,2
%A A050190 _Clark Kimberling_
%E A050190 More terms from _Ralf Stephan_, Aug 18 2004