A106352 Number of compositions of n into 3 parts such that no two adjacent parts are equal.

1, 2, 7, 9, 15, 21, 28, 35, 46, 54, 66, 78, 91, 104, 121, 135, 153, 171, 190, 209, 232, 252, 276, 300, 325, 350, 379, 405, 435, 465, 496, 527, 562, 594, 630, 666, 703, 740, 781, 819, 861, 903, 946, 989, 1036, 1080, 1128, 1176, 1225, 1274, 1327, 1377, 1431

Offset: 4

Author

Christian G. Bower, Apr 29 2005

Keywords

• nonn

Comments

3*a(n) is total number of parts of multiplicity 1 in all compositions of n into 3 parts. - Vladeta Jovovic, Apr 27 2006

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,-1,-1,1).

Crossrefs

Column 3 of A106351. Cf. A003242.

Programs

Mathematica

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 *)

Formula

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