The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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*(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:=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. = 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 Adjacent sequences: A147608 A147609 A147610 * A147612 A147613 A147614 KEYWORD easy,nonn AUTHOR R. J. Mathar, Nov 08 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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