login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113038 Number of ways the set {1,2,...,n} can be split into three subsets of which the sum of one is one more than the equal sums of both other subsets. 1
0, 0, 0, 1, 0, 0, 5, 0, 0, 60, 0, 0, 747, 0, 0, 11076, 0, 0, 183092, 0, 0, 3238140, 0, 0, 60475317, 0, 0, 1175471401, 0, 0, 23600724220, 0, 0, 486653058995, 0, 0, 10260353188386, 0, 0, 220439819437387, 0, 0, 4813287355239594, 0, 0, 106583271423691692, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..100

FORMULA

a(n) is half the coefficient of xy in product(x^(-2k)+x^k(y^k+y^(-k)), k=1..n) for n>1.

EXAMPLE

For n=7 we have splittings 36/27/145, 36/127/45, 136/27/45, 135/27/46, 126/45/37 so a(7) = 5.

MAPLE

A113038:=proc(n) local i, j, p, t; t:= 0; for j from 2 to n do p:=1; for i to j do p:=p*(x^(-2*i)+x^i*(y^i+y^(-i))); od; t:=t, coeff(coeff(p, x, 1), y, 1)/2; od; t; end;

# second Maple program:

b:= proc() option remember; local i, j, t; `if`(args[1]=0, `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(`if`(args[j] -args[nargs] <0, 0, b(sort([seq(args[i] -`if`(i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local m; m:= n*(n+1)/2; `if`(m>3 and irem(m, 3)=1, b(((m-1)/3)$2, (m-1)/3+1, n)/2, 0) end: seq(a(n), n=1..50);  # Alois P. Heinz, Sep 03 2009

CROSSREFS

Cf. A112972.

Sequence in context: A221361 A083527 A221240 * A082512 A068385 A318657

Adjacent sequences:  A113035 A113036 A113037 * A113039 A113040 A113041

KEYWORD

nonn

AUTHOR

Floor van Lamoen, Oct 12 2005

EXTENSIONS

Extended beyond a(25) by Alois P. Heinz, Sep 03 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 15 12:22 EDT 2019. Contains 327078 sequences. (Running on oeis4.)