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 A320315 Number of weakly unimodal compositions of n in which the greatest part occurs exactly four times. 2
 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 46, 62, 87, 116, 160, 212, 288, 380, 508, 666, 883, 1150, 1508, 1954, 2542, 3274, 4229, 5416, 6949, 8856, 11292, 14320, 18162, 22922, 28921, 36344, 45641, 57112, 71407, 88998, 110816, 137600, 170665 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 Wikipedia, Unimodality, Unimodal function FORMULA G.f.: Sum_{n>=0} x^(4*n) / Product_{j=1..n-1} (1-x^j)^2. a(n) ~ Pi^3 * exp(2*Pi*sqrt(n/3)) / (2^5 * 3^(5/4) * n^(11/4)). - Vaclav Kotesovec, Oct 24 2018 MAPLE b:= proc(n, i) option remember; `if`(i>n, 0,       `if`(4*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))     end: a:= n-> `if`(n=0, 1, b(n, 1)): seq(a(n), n=0..70); MATHEMATICA b[n_, i_] := b[n, i] = If[i > n, 0, If[4 i == n, 1, 0] +      Sum[b[n - i j, i + 1] (j + 1), {j, 0, n/i}]]; a[n_] :=  If[n == 0, 1, b[n, 1]]; a /@ Range[0, 70] (* Jean-François Alcover, Apr 22 2021, after Alois P. Heinz *) CROSSREFS Column k=4 of A247255. Sequence in context: A241344 A064428 A052810 * A164090 A029744 A018635 Adjacent sequences:  A320312 A320313 A320314 * A320316 A320317 A320318 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 10 2018 STATUS approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)