The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors 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); MATHEMATICA b[n_, s_, p_] := If[s == p, {s}, If[n < 1, {}, {b[n-1, s, p], If[s-n < p*n, {}, b[n-1, s-n, p*n]]} // Union]]; T[n_] := Sort[b[n, n(n+1)/2, 1] // Flatten] // Union; Array[T, 30] // Flatten (* Jean-François Alcover, Feb 19 2021, after Alois P. Heinz *) 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 19 03:10 EDT 2024. Contains 373492 sequences. (Running on oeis4.)