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A327608 Number of parts in all twice partitions of n where the second partition is strict. 6
0, 1, 3, 8, 17, 34, 74, 134, 254, 470, 842, 1463, 2620, 4416, 7545, 12749, 21244, 34913, 57868, 93583, 151963, 244602, 391206, 620888, 987344, 1550754, 2435087, 3804354, 5920225, 9162852, 14179754, 21785387, 33436490, 51121430, 77935525, 118384318, 179617794 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..4000

EXAMPLE

a(3) = 8 = 1+2+2+3 counting the parts in 3, 21, 2|1, 1|1|1.

MAPLE

g:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

      `if`(n=0, [1, 0], g(n, i-1)+ (f-> f+

       [0, f[1]])(g(n-i, min(n-i, i-1)))))

    end:

b:= proc(n, i) option remember; `if`(n=0, [1, 0],

      `if`(i<2, 0, b(n, i-1)) +(h-> (f-> f +[0, f[1]*

       h[2]/h[1]])(b(n-i, min(n-i, i))*h[1]))(g(i$2)))

    end:

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

seq(a(n), n=0..37);

MATHEMATICA

g[n_, i_] := g[n, i] = If[i(i+1)/2 < n, 0, If[n == 0, {1, 0}, g[n, i - 1] + Function[f, f + {0, f[[1]]}][g[n - i, Min[n - i, i - 1]]]]];

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 2, 0, b[n, i - 1]] + Module[{h, f}, h = g[i, i]; f = b[n - i, Min[n - i, i]] h[[1]]; f + {0, f[[1]] h[[2]]/h[[1]]}]];

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

a /@ Range[0, 37] (* Jean-Fran├žois Alcover, Dec 05 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000009, A000041, A270995, A327554, A327594, A327605, A327607.

Sequence in context: A131253 A145071 A182734 * A239844 A182616 A159217

Adjacent sequences:  A327605 A327606 A327607 * A327609 A327610 A327611

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 18 2019

STATUS

approved

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Last modified May 12 09:16 EDT 2021. Contains 343821 sequences. (Running on oeis4.)