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A106352 Number of compositions of n into 3 parts such that no two adjacent parts are equal. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 15 01:50 EDT 2021. Contains 343909 sequences. (Running on oeis4.)