%I #15 Apr 02 2023 15:16:28

%S 2,6,14,24,46,66,100,138,192,246,324,402,506,612,746,882,1054,1224,

%T 1432,1644,1896,2148,2448,2748,3098,3450,3854,4260,4726,5190,5716,

%U 6246,6840,7434,8100,8766,9506,10248,11066,11886,12790,13692,14680,15672

%N Number of compositions of n into 4 parts such that no two adjacent parts are equal.

%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_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -2, 0, 0, 1, 1, -1).

%F G.f.: (8*x^10+4*x^9+6*x^8+4*x^7+2*x^6) / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

%t Drop[CoefficientList[Series[(8x^10+4x^9+6x^8+4x^7+2x^6)/((1-x)(1-x^2)(1-x^3)(1-x^4)),{x,0,60}],x],6] (* or *) LinearRecurrence[{1,1,0,0,-2,0,0,1,1,-1},{2,6,14,24,46,66,100,138,192,246},60] (* _Harvey P. Dale_, Apr 02 2023 *)

%Y Column 4 of A106351. Cf. A003242.

%K nonn

%O 6,1

%A _Christian G. Bower_, Apr 29 2005