

A026903


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


2



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
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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] (* JeanFrançois Alcover, Sep 28 2019, after Andrew Howroyd *)


PROG

(PARI) a(n)={my(recurse(lim, s1, s2)=if(s2==n, 1, sum(i=1, min((ns2)\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 A068324
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



