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A327554 Number of partitions in all twice partitions of n where the second partition is strict. 4
0, 1, 3, 7, 15, 29, 60, 108, 201, 364, 643, 1106, 1944, 3253, 5493, 9183, 15161, 24727, 40559, 65173, 104963, 167747, 266452, 420329, 663658, 1036765, 1618221, 2514169, 3891121, 5992868, 9224213, 14107699, 21548428, 32798065, 49779331, 75301296, 113757367 (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) = 7 = 1+1+2+3 counting the partitions in 3, 21, 2|1, 1|1|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`(n=0, [1, 0], `if`(i<1, 0,

      b(n, i-1) +(p-> p+[0, p[1]])(g(i)*b(n-i, min(n-i, i)))))

    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[n == 0, {1, 0}, If[i < 1, {0, 0}, b[n, i - 1] + Function[p, p + {0, p[[1]]}][g[i] b[n - i, Min[n - i, i]]]]];

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

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

CROSSREFS

Cf. A000009, A000041, A270995, A327608.

Sequence in context: A283258 A080011 A284022 * A120538 A146019 A284421

Adjacent sequences:  A327551 A327552 A327553 * A327555 A327556 A327557

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 16 2019

STATUS

approved

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Last modified November 27 02:41 EST 2021. Contains 349344 sequences. (Running on oeis4.)