login
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
OFFSET
1,3
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
KEYWORD
nonn
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