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A328042 Number of parts in all proper twice partitions of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Dec 10 2020, after Alois P. Heinz *)

CROSSREFS

Column k=2 of A327631.

Cf. A327769.

Sequence in context: A181156 A162394 A129212 * A331082 A117984 A050615

Adjacent sequences:  A328039 A328040 A328041 * A328043 A328044 A328045

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 02 2019

STATUS

approved

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Last modified May 14 22:40 EDT 2021. Contains 343909 sequences. (Running on oeis4.)