A161943 Number of different equations that can be made by summing numbers from 1 to n and using every number not more than once.

0, 0, 1, 3, 7, 17, 43, 108, 273, 708, 1867, 4955, 13256, 35790, 97340, 266240, 732014, 2022558, 5612579, 15634288, 43702232, 122550885, 344661924, 971908613, 2747404212, 7784038617, 22100387619, 62869809733, 179173559128, 511497066733, 1462522478549, 4188024794407

Offset

1,4

Comments

The summands of each side are in increasing order and the minimum of all summands is on the left side.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..940

Formula

a(n) ~ 3^(n+1) / (4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Sep 11 2014

Example

a(3) = 1, as the only equation we can make by summing numbers from the set {1, 2, 3} is 1+2=3. a(4) = 3, as we can make three equations: 1+2=3, 1+3=4, 1+4=2+3.

Maple

b:= proc(n, i) option remember; local m; m:= i*(i+1)/2;
      if n>m then 0
    elif n=m then 1
    else b(n, i-1) +b(abs(n-i), i-1) +b(n+i, i-1)
      fi
    end:
a:= proc(n) option remember;
      `if`(n>2, b(n, n-1)+ a(n-1), 0)
    end:
seq(a(n), n=1..40); # Alois P. Heinz, Aug 31 2009, revised Sep 16 2011

Mathematica

Table[(Length[ Select[Range[0, 3^n - 1], Apply[Plus, Pick[Range[n], PadLeft[IntegerDigits[ #, 3], n], 1]] == Apply[Plus, Pick[Range[n], PadLeft[IntegerDigits[ #, 3], n], 2]] &]] - 1)/ 2, {n, 14}]

Crossrefs

Column k=2 of A196231.

Sequence in context: A335596 A238824 A340766 * A134184 A142975 A211277

Adjacent sequences: A161940 A161941 A161942 * A161944 A161945 A161946

Keyword

nonn

Author

Tanya Khovanova, Jun 22 2009

Extensions

More terms from Alois P. Heinz, Aug 31 2009

Status

approved