The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A160438 Number of partitions of n*(n+1)/2 with at most four parts that can be obtained from grouping (with parentheses) a permutation of the sum 1+2+...+n 3
 1, 1, 2, 5, 13, 35, 93, 215, 437, 815, 1436, 2413, 3886, 6041, 9125, 13436, 19323, 27221, 37670, 51293, 68797, 91025, 118982, 153797, 196721, 249206, 312935, 389761, 481709, 591080, 720485, 872763, 1050980, 1258565, 1499351, 1777462 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the number of integer quadruples (x,y,z,w) with x >= y >= z >= w >= 0 and x+y+z+w = n*(n+1)/2 such that the set {1,2,...,n} can be partitioned into four (possibly empty) subsets with respective element sums x, y, z, w. LINKS H. v. Eitzen, How to Build Triangles from Integers FORMULA If n >= 8 then a(n) = A001400(n*(n+1)/2) - 2*A011848(n+1) - 5. EXAMPLE For n = 3 the a(3) = 5 solutions are 6 = (1+2+3), 5+1 = (2+3)+(1), 4+2 = (1+3)+(2), 3+3 = (3)+(1+2), 3+2+1 = (3)+(2)+(1). Note that 3+3 = (1+2)+(3) is the same as (3)+(1+2) as both are 3+3. For n = 6 the partition 10+4+4+3 is *not* among the a(6) = 93 solutions because 4 can only come from grouping either (4) or (1+3), hence both groupings would have to occur; but (1+3) conflicts with both possible groupings (3) and (1+2) which could produce 3. CROSSREFS Sequence in context: A048781 A291242 A097919 * A335725 A240609 A054657 Adjacent sequences:  A160435 A160436 A160437 * A160439 A160440 A160441 KEYWORD nonn AUTHOR Hagen von Eitzen, May 13 2009 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 June 21 12:19 EDT 2021. Contains 345364 sequences. (Running on oeis4.)