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%I #7 Jul 17 2016 07:04:00
%S 1,2,5,18,53,162,505,1548,4756,14650,45065,138622,426528,1312242,
%T 4037155,12420806,38213753,117567880,361708733,1112830322,3423724282,
%U 10533403974,32406988208,99703082744,306745721586,943731474930
%N The number of 2-compositions of n of Carlitz type.
%H E. Munarini, M. Poneti, S. Rinaldi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Rinaldi/rinaldi.html">Matrix compositions</a>, JIS 12 (2009) 09.4.8, Table 3.
%p m := 2 ;
%p kmax := 30 ;
%p add((-1)^k*(1-(1-x^k)^m)/(1-x^k)^m,k=1..kmax) ;
%p 1/(1+%) ;
%p taylor(%,x=0,kmax-1) ;
%p gfun[seriestolist](%) ;
%Y Cf. A003242 (1-compositions).
%K nonn
%O 0,2
%A _R. J. Mathar_, Jul 15 2016