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A327594 Number of parts in all twice partitions of n. 6
0, 1, 5, 14, 44, 100, 274, 581, 1417, 2978, 6660, 13510, 29479, 58087, 120478, 236850, 476913, 916940, 1812498, 3437043, 6657656, 12512273, 23780682, 44194499, 83117200, 152837210, 283431014, 517571202, 949844843, 1719175176, 3127751062, 5618969956, 10133425489 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3200

EXAMPLE

a(2) = 5 = 1+2+2 counting the parts in 2, 11, 1|1.

a(3) = 14 = 1+2+3+2+3+3: 3, 21, 111, 2|1, 11|1, 1|1|1.

MAPLE

g:= proc(n) option remember; (p-> [p(n), add(p(n-j)*

      numtheory[tau](j), j=1..n)])(combinat[numbpart])

    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)))

    end:

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

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

# second Maple program:

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-> b(n$2, 2)[2]:

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

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_] := b[n, n, 2][[2]];

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

CROSSREFS

Cf. A000041, A006128, A063834, A327590, A327605, A327607, A327608.

Column k=2 of A327618.

Sequence in context: A120901 A222988 A349222 * A034530 A125246 A302762

Adjacent sequences:  A327591 A327592 A327593 * A327595 A327596 A327597

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 18 2019

STATUS

approved

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Last modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)