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A050190 T(n,5), array T as in A050186; a count of aperiodic binary words. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 19:05 EDT 2021. Contains 346441 sequences. (Running on oeis4.)