%I #10 Apr 28 2022 20:21:56

%S 1,2,7,9,15,21,28,35,46,54,66,78,91,104,121,135,153,171,190,209,232,

%T 252,276,300,325,350,379,405,435,465,496,527,562,594,630,666,703,740,

%U 781,819,861,903,946,989,1036,1080,1128,1176,1225,1274,1327,1377,1431

%N Number of compositions of n into 3 parts such that no two adjacent parts are equal.

%C 3*a(n) is total number of parts of multiplicity 1 in all compositions of n into 3 parts. - _Vladeta Jovovic_, Apr 27 2006

%H A. Knopfmacher and H. Prodinger, <a href="http://dx.doi.org/10.1006/eujc.1998.0216">On Carlitz compositions</a>, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).

%F G.f. x^4*(1+4*x^2-3*x^3+4*x^4)/((1-x^6)*(1-x)^2).

%t Drop[CoefficientList[Series[x^4(1+4x^2-3x^3+4x^4)/((1-x^6)(1-x)^2),{x,0,60}],x],4] (* or *) LinearRecurrence[{1,1,0,-1,-1,1},{1,2,7,9,15,21},60] (* _Harvey P. Dale_, May 13 2018 *)

%Y Column 3 of A106351. Cf. A003242.

%K nonn

%O 4,2

%A _Christian G. Bower_, Apr 29 2005