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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

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OFFSET

4,2

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

Table of n, a(n) for n=4..56.

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).

FORMULA

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

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 *)

CROSSREFS

Column 3 of A106351. Cf. A003242.

Sequence in context: A294863 A085544 A154789 * A098017 A225675 A185869

Adjacent sequences: A106349 A106350 A106351 * A106353 A106354 A106355

KEYWORD

nonn

AUTHOR

Christian G. Bower, Apr 29 2005

STATUS

approved