A026903 a(n) is the number of multisets S of positive integers satisfying E(S)=n, where E = 2nd elementary symmetric function.

1, 1, 2, 2, 2, 3, 2, 3, 4, 3, 3, 5, 3, 4, 6, 4, 4, 6, 4, 6, 7, 4, 5, 9, 6, 6, 8, 6, 7, 9, 5, 9, 10, 6, 9, 12, 6, 8, 12, 9, 9, 12, 8, 11, 14, 8, 10, 15, 11, 12, 13, 10, 13, 16, 11, 15, 16, 8, 14, 21, 12, 14, 19, 14, 16, 18, 12, 17, 21, 14, 17, 23, 15, 19, 22

Offset

1,3

Links

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

Wikipedia, Elementary symmetric polynomial

Example

a(9) = 4 counts {1,9}, {3,3}, {1,1,4}, {1,1,1,2}.
a(33) = 10 counts {1,1,1,1,1,1,3}, {1,1,1,2,2,2}, {1,1,1,10}, {1,1,2,7}, {1,1,4,4}, {1,1,16}, {1,2,2,5}, {1,33}, {3,3,4}, {3,11}.

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]}]]; Sum[r[i, i, 0], {i, 1, n}]];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 28 2019, after Andrew Howroyd *)

Prog

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

Crossrefs

Cf. A026904.

Sequence in context: A330861 A286565 A219354 * A253893 A289437 A348369

Adjacent sequences: A026900 A026901 A026902 * A026904 A026905 A026906

Keyword

nonn

Author

Clark Kimberling

Extensions

a(33) corrected by Laurance L. Y. Lau, Dec 17 2018

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

Status

approved