A106353 Number of compositions of n into 4 parts such that no two adjacent parts are equal.

2, 6, 14, 24, 46, 66, 100, 138, 192, 246, 324, 402, 506, 612, 746, 882, 1054, 1224, 1432, 1644, 1896, 2148, 2448, 2748, 3098, 3450, 3854, 4260, 4726, 5190, 5716, 6246, 6840, 7434, 8100, 8766, 9506, 10248, 11066, 11886, 12790, 13692, 14680, 15672

Offset: 6

Author

Christian G. Bower, Apr 29 2005

Keywords

• nonn

Links

• A. Knopfmacher and H. Prodinger, On Carlitz compositions, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.
• Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -2, 0, 0, 1, 1, -1).

Crossrefs

Column 4 of A106351. Cf. A003242.

Programs

Mathematica

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 *)

Formula

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)).