This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A213238 Triangle T(n,k) in which n-th row lists in increasing order the distinct values v satisfying v = sum of elements in S = product of elements in P for a partition of {1,...,n} into two sets S and P. 2
 1, 3, 8, 12, 18, 24, 32, 40, 42, 50, 60, 64, 72, 84, 88, 90, 98, 99, 105, 112, 120, 128, 130, 135, 144, 162, 168, 180, 182, 192, 200, 208, 210, 220, 231, 242, 252, 264, 266, 272, 280, 288, 294, 300, 312, 315, 320, 324, 330, 338, 340, 360, 364, 378, 392, 400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Rows n = 1..798, flattened FORMULA T(n,1) = floor((n-1)^2/2) = A007590(n-1) for n>=5. EXAMPLE For n=1 v=1 satisfies the condition with S={1}, P={} => row 1 = [1]. For n=2 no v can be found => row 2 is empty: []. For n=3 there is one solution: S={1,2}, P={3}, v=3 => row 3 = [3]. For n=10 we have three partitions of {1,2,...,10} into S and P satisfying v = Sum_{i:S} i = Product_{k:P} k but there are only two distinct values v: S={2,3,5,6,7,8,9}, P={1,4,10}, v=40; S={4,5,6,8,9,10}, P={1,2,3,7}, v=42; S={1,2,3,4,5,8,9,10}, P={6,7}, v=42 => row 10 = [40, 42]. Triangle T begins: 1; ; 3; ; 8; 12; 18; 24; 32; 40, 42; 50; 60, 64; 72; 84, 88, 90; MAPLE b:= proc(n, s, p)       `if`(s=p, {s}, `if`(n<1, {}, {b(n-1, s, p)[],       `if`(s-n sort([b(n, n*(n+1)/2, 1)[]])[]: seq(T(n), n=1..30); CROSSREFS Row lengths (or number of solutions) are in A213237. T(n,1) = A007590(n-1) for n>=5. Sequence in context: A256711 A219635 A063225 * A005660 A086813 A287081 Adjacent sequences:  A213235 A213236 A213237 * A213239 A213240 A213241 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Jun 07 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)