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

Author

Christian G. Bower, Apr 29 2005

Keywords

• nonn
• easy

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

Crossrefs

Column 5 of A106351. Cf. A003242.

Programs

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 *)

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]