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A026904 Number of sets S of positive integers satisfying E(S)=n, where E = 2nd elementary symmetric function. 2
0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 3, 2, 2, 2, 3, 2, 4, 2, 2, 3, 4, 1, 4, 3, 3, 3, 4, 3, 4, 2, 3, 5, 5, 1, 4, 4, 4, 5, 4, 2, 6, 3, 3, 6, 5, 3, 5, 4, 4, 4, 6, 4, 8, 2, 2, 8, 6, 3, 5, 6, 4, 6, 6, 3, 7, 4, 5, 9, 6, 3, 6, 6, 6, 7, 4, 5, 9, 5, 3, 9, 9, 3, 7, 6, 4, 10, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Wikipedia, Elementary symmetric polynomial

EXAMPLE

a(2) = 2 counts {1,11}, {1,2,3}.

MATHEMATICA

a[n_] := Module[{r}, r[lim_, s1_, s2_] := r[lim, s1, s2] = If[s2 == n, 1, Sum[r[i, s1 + i, s2 + s1*i], {i, 1, Min[Quotient[n-s2, s1], lim - 1]}]]; Sum[r[i, i, 0], {i, 1, n}]];

a /@ Range[1, 100] (* Jean-François Alcover, Sep 28 2019, after Andrew Howroyd *)

PROG

a(n)={my(recurse(lim, s1, s2)=if(s2==n, 1, sum(i=1, min((n-s2)\s1, lim-1), self()(i, s1+i, s2+s1*i)))); sum(i=1, n, recurse(i, i, 0))} \\ Andrew Howroyd, Dec 17 2018

CROSSREFS

Cf. A026903.

Sequence in context: A322873 A332897 A349552 * A057828 A082498 A112223

Adjacent sequences: A026901 A026902 A026903 * A026905 A026906 A026907

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Terms a(35) and beyond from Andrew Howroyd, Dec 17 2018

STATUS

approved

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Last modified February 1 06:22 EST 2023. Contains 359981 sequences. (Running on oeis4.)