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A094188
Number of levels in the compositions of n with odd summands.
0
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
OFFSET
2,3
LINKS
S. Heubach and T. Mansour, Counting rises, levels and drops in compositions, arXiv:math/0310197 [math.CO], 2003.
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
KEYWORD
nonn
AUTHOR
Ralf Stephan, May 25 2004
STATUS
approved