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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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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].

Felix Pahl, Find the number of n-length Lyndon words on alphabet {0,1} with k blocks of 0's. (answer), Mathematics StackExchange, 2020.

Index entries for linear recurrences with constant coefficients, signature (4,-6,6,-9,12,-9,6,-6,4,-1).

FORMULA

G.f.: x^4(2x^2-x+2)/((1-x)^6*(1+x+x^2)^2).

MATHEMATICA

CoefficientList[Series[x^4(2*x^2 - x + 2)/((1-x)^6 * (1 + x + x^2)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2012 *)

CROSSREFS

Cf. A006584 (2nd Witt transform of A000027).

Sequence in context: A055503 A077802 A095151 * A007991 A037294 A076857

Adjacent sequences:  A147608 A147609 A147610 * A147612 A147613 A147614

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Nov 08 2008

STATUS

approved

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Last modified May 26 11:30 EDT 2022. Contains 354086 sequences. (Running on oeis4.)