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 A161943 Number of different equations that can be made by summing numbers from 1 to n and using every number not more than once. 13
 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 (list; graph; refs; listen; history; text; internal format)
 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: A191627 A178778 A238824 * 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

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)