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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-Fran├žois 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.)