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A094188

Number of levels in the compositions of n with odd summands.

1, 0, 3, 2, 8, 10, 23, 36, 69, 116, 208, 356, 621, 1064, 1831, 3126, 5336, 9070, 15395, 26060, 44041, 74280, 125088, 210312, 353113, 592080, 991563, 1658666, 2771624, 4626706, 7716143, 12857076, 21405261, 35608604, 59192176, 98325356

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OFFSET

2,3

LINKS

Table of n, a(n) for n=2..37.

S. Heubach and T. Mansour, Counting rises, levels and drops in compositions, arXiv:math/0310197 [math.CO], 2003.

Index entries for linear recurrences with constant coefficients, signature (1, 3, -1, -3, -1).

FORMULA

G.f.: (x^2(1-x^2))/((1+x)^2(1-x-x^2)^2).

a(n) = (1/5) * [3nF(n)-4nF(n-1)+7F(n)-10F(n-1)+10(-1)^n], F(n)=A000045(n).

a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 3*a(n-4) - a(n-5). - Wesley Ivan Hurt, Apr 19 2023

MATHEMATICA

LinearRecurrence[{1, 3, -1, -3, -1}, {1, 0, 3, 2, 8, 10}, 36] (* Jean-François Alcover, Jan 21 2019 *)

CROSSREFS

Cf. A000045.

Sequence in context: A163356 A209360 A095013 * A088551 A373288 A301903

Adjacent sequences: A094185 A094186 A094187 * A094189 A094190 A094191

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 25 2004

STATUS

approved

URL: https://oeis.org/A094188

⇱ A094188 - OEIS