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A147611 The 3rd Witt transform of A000027. 1
0, 0, 0, 0, 2, 7, 18, 42, 84, 153, 264, 429, 666, 1001, 1456, 2061, 2856, 3876, 5166, 6783, 8778, 11214, 14168, 17710, 21924, 26910, 32760, 39582, 47502, 56637, 67122, 79112, 92752, 108207, 125664, 145299, 167310, 191919, 219336, 249795, 283556 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
a(n) is the number of binary Lyndon words of length n+3 having 3 blocks of 0's, see Math.SE. - Andrey Zabolotskiy, Nov 16 2021
LINKS
Pieter Moree, The formal series Witt transform, Discr. Math. no. 295 vol. 1-3 (2005) 143-160.
Pieter Moree, Convoluted convolved Fibonacci numbers, arXiv:math/0311205 [math.CO].
FORMULA
G.f.: x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2).
a(n) = (1/27)*((3*A049347(n) + A049347(n-1)) - 3*(-1)^n*(A099254(n) - A099254(n- 1)) + n*(3*n^4 - 15*n^2 - 28)/40). - G. C. Greubel, Oct 24 2022
MATHEMATICA
CoefficientList[Series[x^4(2 -x+ 2*x^2)/((1-x)^6*(1 +x +x^2)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 13 2012 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0, 0, 0, 0] cat Coefficients(R!( x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2) )); // G. C. Greubel, Oct 24 2022
(SageMath)
def A147611_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^4*(2-x+2*x^2)/((1-x)^6*(1+x+x^2)^2) ).list()
A147611_list(50) # G. C. Greubel, Oct 24 2022
CROSSREFS
Cf. A006584 (2nd Witt transform of A000027), A049347, A099254, A147618.
Sequence in context: A055503 A077802 A095151 * A007991 A037294 A076857
KEYWORD
easy,nonn
AUTHOR
R. J. Mathar, Nov 08 2008
STATUS
approved

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Last modified March 3 00:46 EST 2024. Contains 370499 sequences. (Running on oeis4.)