A244239 Number of partitions of n into 3 parts such that every i-th smallest part (counted with multiplicity) is different from i.

1, 3, 4, 6, 7, 9, 11, 13, 15, 18, 20, 23, 26, 29, 32, 36, 39, 43, 47, 51, 55, 60, 64, 69, 74, 79, 84, 90, 95, 101, 107, 113, 119, 126, 132, 139, 146, 153, 160, 168, 175, 183, 191, 199, 207, 216, 224, 233, 242, 251, 260, 270, 279, 289, 299, 309, 319, 330, 340

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).

Formula

From Chai Wah Wu, Apr 18 2024: (Start)

a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) for n > 15.

G.f.: x^9*(-x^6 + 2*x^4 + x^3 - 2*x - 1)/((x - 1)^3*(x + 1)*(x^2 + x + 1)). (End)

Maple

a:= proc(n) option remember; `if`(n<14, [1, 3, 4, 6, 7][n-8],
      ((-4*n+56)*a(n-5) +(3*n-16)*a(n-4) +(7*n-66)*a(n-3)
      +(4*n-44)*a(n-2) +(28-3*n)*a(n-1)) / (7*n-78))
    end:
seq(a(n), n=9..80);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, Function[p, Expand[x*(p-Coefficient[p, x, i-1]*x^(i-1))]][b[n-i, i]]]]];
a[n_] := Coefficient[b[n, n], x, 3];
Table[a[n], {n, 9, 80}] (* Jean-François Alcover, May 01 2018, after Alois P. Heinz *)

Crossrefs

Column k=3 of A238406.

Sequence in context: A236444 A286809 A352178 * A006855 A301766 A229173

Adjacent sequences: A244236 A244237 A244238 * A244240 A244241 A244242

Keyword

nonn,changed

Author

Alois P. Heinz, Jun 23 2014

Status

approved