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

0, 6, 21, 56, 126, 250, 462, 792, 1287, 2002, 3000, 4368, 6188, 8568, 11628, 15500, 20349, 26334, 33649, 42504, 53125, 65780, 80730, 98280, 118755, 142500, 169911, 201376, 237336, 278256, 324625, 376992, 435897, 501942

Offset

5,2

Links

G. C. Greubel, Table of n, a(n) for n = 5..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,2,-8,12,-8,2,-1,4,-6,4, -1).

Formula

a(n) = n * A051170(n).

From Ralf Stephan, Aug 18 2004: (Start)

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)

a(n) = A000389(n) - [5 divides n]*n/5.

a(n) = n*floor(C(n-1, 4)/5). (End)

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

Mathematica

Table[n*Floor[Binomial[n - 1, 4]/5], {n, 5, 50}] (* G. C. Greubel, Nov 25 2017 *)
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 *)

Prog

(PARI) for(n=5, 40, print1(n*floor(binomial(n-1, 4)/5), ", ")) \\ G. C. Greubel, Nov 25 2017
(Magma) [n*floor(Binomial(n-1, 4)/5): n in [5..40]]; // G. C. Greubel, Nov 25 2017
(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

Crossrefs

Cf. A000389, A050186.

Sequence in context: A292950 A282845 A341135 * A008498 A015640 A138780

Adjacent sequences: A050187 A050188 A050189 * A050191 A050192 A050193

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Ralf Stephan, Aug 18 2004

Status

approved