A328042 Number of parts in all proper twice partitions of n.

3, 21, 61, 205, 474, 1246, 2723, 6277, 12961, 28682, 56976, 118919, 234715, 473988, 913011, 1807211, 3430048, 6648397, 12500170, 23764885, 44174088, 83090853, 152803509, 283387971, 517516615, 949775754, 1719088271, 3127641937, 5618833687, 10133255636

Offset

3,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 3..5000 (terms 3..2000 from Alois P. Heinz)

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
     `if`(k=0, [1, 1], `if`(i<2, 0, b(n, i-1, k))+
         (h-> (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*
        b(n-i, min(n-i, i), k)))(b(i$2, k-1))))
    end:
a:= n-> (k-> add(b(n$2, i)[2]*(-1)^(k-i)*binomial(k, i), i=0..k))(2):
seq(a(n), n=3..35);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[k == 0, {1, 1}, If[i < 2, 0, b[n, i - 1, k]] + Function[h, Function[f, f + {0, f[[1]] h[[2]]/ h[[1]]}][h[[1]] b[n - i, Min[n - i, i], k]]][b[i, i, k - 1]]]];
a[n_] := With[{k = 2}, Sum[b[n, n, i][[2]] (-1)^(k-i) Binomial[k, i], {i, 0, k}]];
a /@ Range[3, 35] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)

Crossrefs

Column k=2 of A327631.

Cf. A327769.

Sequence in context: A162394 A129212 A354850 * A331082 A117984 A050615

Adjacent sequences: A328039 A328040 A328041 * A328043 A328044 A328045

Keyword

nonn

Author

Alois P. Heinz, Oct 02 2019

Status

approved