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A327553 Number of partitions in all twice partitions of n where both partitions are strict. 4
0, 1, 1, 4, 6, 11, 20, 33, 57, 100, 165, 254, 417, 649, 1039, 1648, 2540, 3836, 6020, 9035, 13645, 20752, 31054, 45993, 68668, 101511, 149525, 220132, 321614, 468031, 684124, 989703, 1427054, 2064859, 2964987, 4254028, 6090453, 8686574, 12366583, 17598885 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

EXAMPLE

a(3) = 4 = 1+1+2 counting the partitions in 3, 21, 2|1.

MAPLE

g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(

     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)

    end:

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]])(

       g(i)*b(n-i, min(n-i, i-1)))))

    end:

a:= n-> b(n$2)[2]:

seq(a(n), n=0..42);

MATHEMATICA

g[n_] := g[n] = If[n == 0, 1, Sum[g[n - j] Sum[If[OddQ[d], d, 0], {d, Divisors[j]}], {j, 1, n}]/n];

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]]}][g[i] b[n-i, Min[n-i, i-1]]]]];

a[n_] := b[n, n][[2]];

a /@ Range[0, 42] (* Jean-Fran├žois Alcover, Dec 18 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000009, A279785, A327605.

Sequence in context: A047811 A244010 A154145 * A302428 A336142 A091280

Adjacent sequences:  A327550 A327551 A327552 * A327554 A327555 A327556

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 16 2019

STATUS

approved

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Last modified January 21 23:44 EST 2022. Contains 350481 sequences. (Running on oeis4.)