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<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).

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)

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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 *)

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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);

Alois P. Heinz, <a href="/A244239/b244239.txt">Table of n, a(n) for n = 9..1000</a>

allocated for Alois P. Heinz

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

9,2

Column k=3 of A238406.

allocated

nonn

Alois P. Heinz, Jun 23 2014

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