A106354 Number of compositions of n into 5 parts such that no two adjacent parts are equal.

1, 3, 15, 30, 68, 119, 204, 316, 489, 696, 987, 1340, 1801, 2348, 3035, 3833, 4812, 5935, 7273, 8792, 10576, 12576, 14887, 17465, 20401, 23651, 27319, 31349, 35861, 40791, 46260, 52212, 58776, 65881, 73667, 82068, 91225, 101067, 111748, 123185

Offset

7,2

Links

Table of n, a(n) for n=7..46.

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,-1,-1,-1,1,1,1,0,0,-1,-1,1).

Formula

G.f.: -x^7*(16*x^8 +12*x^7 +21*x^6 +22*x^5 +23*x^4 +12*x^3 +11*x^2 +2*x +1) / ((x -1)^5*(x +1)^2*(x^2 +1)*(x^2 +x +1)*(x^4 +x^3 +x^2 +x +1)). [Colin Barker, Feb 13 2013]

Mathematica

LinearRecurrence[{1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, -1, -1, 1}, {1, 3, 15, 30, 68, 119, 204, 316, 489, 696, 987, 1340, 1801, 2348, 3035}, 40] (* Harvey P. Dale, Dec 15 2013 *)

Crossrefs

Column 5 of A106351. Cf. A003242.

Sequence in context: A298088 A290325 A271326 * A228308 A018972 A289962

Adjacent sequences: A106351 A106352 A106353 * A106355 A106356 A106357

Keyword

nonn,easy

Author

Christian G. Bower, Apr 29 2005

Status

approved