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

6,1

Links

Table of n, a(n) for n=6..49.

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).

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)).

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 *)

Crossrefs

Column 4 of A106351. Cf. A003242.

Sequence in context: A109592 A238410 A256482 * A002703 A230978 A112853

Adjacent sequences: A106350 A106351 A106352 * A106354 A106355 A106356

Keyword

nonn

Author

Christian G. Bower, Apr 29 2005

Status

approved