|
| |
|
|
A110610
|
|
Maximal value of sum(p(i)p(i+1),i=1..n), where p(n+1)=p(1), as p ranges over all permutations of {1,2,...,n}.
|
|
2
| |
|
|
1, 4, 11, 25, 48, 82, 129, 191, 270, 368, 487, 629, 796, 990, 1213, 1467, 1754, 2076, 2435, 2833, 3272, 3754, 4281, 4855, 5478, 6152, 6879, 7661, 8500, 9398, 10357, 11379, 12466, 13620, 14843, 16137, 17504, 18946, 20465, 22063, 23742, 25504
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| The Fifty-Seventh William Lowell Putnam Competition, Amer. Math. Monthly, 104, 1997, 744-754, Problem B-3.
V. Mihai, Problem 10725, Amer. Math. Monthly, 108 (March 2001), pp. 272-273.
|
|
|
FORMULA
| a(1)=1; a(n)=(2n^3+3n^2-11n+18)/6 for n>=2.
|
|
|
EXAMPLE
| a(4)=25 because the values of the sum for the permutations of {1,2,3,4} are 21 (8 times), 24 (8 times) and 25 (8 times).
|
|
|
MAPLE
| a:=proc(n) if n=1 then 1 else (2*n^3+3*n^2-11*n+18)/6 fi end: seq(a(n), n=1..50);
|
|
|
CROSSREFS
| Cf. A016825, A110611.
Sequence in context: A192597 A176959 A115294 * A051462 A006004 A006522
Adjacent sequences: A110607 A110608 A110609 * A110611 A110612 A110613
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 30 2005
|
| |
|
|
