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A326441 Number of subsets of {1..n} whose sum is equal to the product of their complement. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 5 16:55 EDT 2022. Contains 357259 sequences. (Running on oeis4.)