A326441 Number of subsets of {1..n} whose sum is equal to the product of their complement.

0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 4, 4, 3, 2, 2, 4, 3, 5, 3, 2, 4, 5, 4, 5, 6, 1, 4, 2, 5, 4, 7, 4, 4, 3, 3, 6, 14, 3, 4, 10, 6, 3, 6, 4, 4, 4, 8, 7, 6, 8, 7, 10, 5, 11, 8, 5, 11, 4, 7, 7, 5, 8, 12, 5, 6, 9, 8, 11, 8, 5, 8, 9, 8, 10, 8

Offset

0,11

Comments

Essentially the same as A178830. - R. J. Mathar, Jul 12 2019

Links

Giovanni Resta, Table of n, a(n) for n = 0..500

Example

The initial terms count the following subsets:
   1: {1}
   3: {1,2}
   5: {3,5}
   6: {3,4,5}
   7: {2,4,5,7}
   8: {2,4,5,6,7}
   9: {2,3,5,6,7,9}
  10: {4,5,6,8,9,10}
  10: {2,3,5,6,7,8,9}
  10: {1,2,3,4,5,8,9,10}
Also the number of subsets of {1..n} whose product is equal to the sum of their complement. For example, the initial terms count the following subsets:
   1: {}
   3: {3}
   5: {1,2,4}
   6: {1,2,6}
   7: {1,3,6}
   8: {1,3,8}
   9: {1,4,8}
  10: {6,7}
  10: {1,4,10}
  10: {1,2,3,7}

Maple

b:= proc(n, s, p)
      `if`(s=p, 1, `if`(n<1, 0, b(n-1, s, p)+
      `if`(s-n<p*n, 0, b(n-1, s-n, p*n))))
    end:
a:= n-> b(n, n*(n+1)/2, 1):
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 12 2019

Mathematica

Table[Length[Select[Subsets[Range[n]], Plus@@#==Times@@Complement[Range[n], #]&]], {n, 0, 10}]

Crossrefs

Cf. A028422, A053632, A059529, A063865, A178830, A301987, A325044, A325538, A326172, A326173, A326174, A326175, A326179, A326180.

Sequence in context: A146969 A338804 A090270 * A178830 A029329 A287872

Adjacent sequences: A326438 A326439 A326440 * A326442 A326443 A326444

Keyword

nonn

Author

Gus Wiseman, Jul 07 2019

Extensions

a(21)-a(83) from Giovanni Resta, Jul 08 2019

Status

approved