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A327552
Number of partitions in all twice partitions of n where the first partition is strict.
4
0, 1, 2, 7, 11, 29, 63, 125, 225, 489, 930, 1704, 3260, 5859, 10868, 20026, 35062, 61660, 111789, 191119, 337432, 585847, 1003876, 1705380, 2921394, 4930357, 8311554, 14013583, 23435178, 38849655, 64847870, 106784912, 175699558, 289676875, 472418418, 772944773
OFFSET
0,3
LINKS
EXAMPLE
a(3) = 7 = 1+1+1+2+2 counting the partitions in 3, 21, 111, 2|1, 11|1.
MAPLE
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, [1, 0], b(n, i-1)+(p->p+[0, p[1]])(
combinat[numbpart](i)*b(n-i, min(n-i, i-1)))))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..36);
MATHEMATICA
b[n_, i_] := b[n, i] = If[i(i+1)/2<n, {0, 0}, If[n==0, {1, 0}, b[n, i-1] + Function[p, p + {0, p[[1]]}][PartitionsP[i] b[n-i, Min[n-i, i-1]]]]];
a[n_] := b[n, n][[2]];
a /@ Range[0, 36] (* Jean-François Alcover, Dec 17 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 16 2019
STATUS
approved