|
Search: id:A084399
|
|
|
| A084399 |
|
Consider the set N = {1,2,3,...,n}; let S and S' be subsets of N such that S union S' is N. Define prod(S) = ( sum of members of S)*( sum of members of S'); then a(n) = sum of all possible prod(S). |
|
+0
1
|
|
| 0, 2, 22, 140, 680, 2800, 10304, 34944, 111360, 337920, 985600, 2782208, 7641088, 20500480, 53903360, 139264000, 354287616, 889061376, 2203975680, 5404098560, 13120307200, 31569477632, 75342282752, 178467635200, 419849830400
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
EXAMPLE
|
For n = 4, N = {1,2,3,4}, the 5 columns below give S sum(S) S' sum(S') prod(S):
{ } 0 {1,2,3,4} 10 0
{1) 1 {2,3,4} 9 9
(2) 2 {1,3,4} 8 16
{3} 3 {1,2,4} 7 21
{4} 4 {1,2,3} 6 24
{1,2} 3 {3,4} 7 21
{1,3} 4 {2,4} 6 24
{1,4} 5 {2,3} 5 25
Sum of all prod(S) = 140 hence a(4) = 140.
|
|
PROGRAM
|
(PARI) print(0); LIMIT = 40; V = vector(LIMIT*(LIMIT + 1)/2); V[1] = 1; for (i = 2, LIMIT, forstep (j = i*(i - 1)/2, 1, -1, V[i + j] += V[j]); V[i]++; k = i*(i + 1)/2; s = sum(j = 1, (k - 1)\2, j*(k - j)*V[j]); if (!(k%2), s += k*k*V[k\2]/8); print(s)); (Wasserman)
|
|
CROSSREFS
|
Sequence in context: A083833 A062180 A067057 this_sequence A123960 A091169 A000184
Adjacent sequences: A084396 A084397 A084398 this_sequence A084400 A084401 A084402
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 31 2003
|
|
EXTENSIONS
|
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Dec 22 2004
|
|
|
Search completed in 0.002 seconds
|
