A006980 - OEIS

%I M1411 #30 Feb 07 2024 09:31:32

%S 1,2,5,12,28,64,143,315,687,1485,3186,6792,14401,30391,63872,133751,

%T 279177,581040,1206151,2497895,5161982,10646564,21919161,45052841,

%U 92461171,189489255,387830160,792810956,1618840800,3301999647

%N Compositions: 6th column of A048004.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D J. L. Yucas, Counting special sets of binary Lyndon words, Ars Combin., 31 (1991), 21-29.

%H Alois P. Heinz, <a href="/A006980/b006980.txt">Table of n, a(n) for n = 6..1000</a>

%H J. L. Yucas, <a href="/A006980/a006980.pdf">Counting special sets of binary Lyndon words</a>, Ars Combin., 31 (1991), 21-29. (Annotated scanned copy)

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-1,-2,-4,-5,-4,-3,-2,-1).

%F G.f.: x^6 / ((1-x-x^2-x^3-x^4-x^5) * (1-x-x^2-x^3-x^4-x^5-x^6)). - _Alois P. Heinz_, Oct 29 2008

%p a:= n-> (Matrix(11, (i,j)-> if i=j-1 then 1 elif j=1 then [2, 1, 0, -1, -2, -4, -5, -4, -3, -2, -1][i] else 0 fi)^n) [1,7]: seq(a(n), n=6..40); # _Alois P. Heinz_, Oct 29 2008

%o (PARI) Vec(1/(1-x-x^2-x^3-x^4-x^5)/(1-x-x^2-x^3-x^4-x^5-x^6)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 10 2013

%Y Cf. A048004.

%K nonn,easy

%O 6,2

%A _Simon Plouffe_

%E Corrected definition: 6th column of A048004. - _Geoffrey Critzer_, Nov 09 2008