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Search: id:A110610
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| A110610 |
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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}. |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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REFERENCES
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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.
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FORMULA
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a(1)=1; a(n)=(2n^3+3n^2-11n+18)/6 for n>=2.
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EXAMPLE
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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).
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MAPLE
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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);
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CROSSREFS
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Cf. A016825, A110611.
Sequence in context: A159348 A159349 A115294 this_sequence A051462 A006004 A006522
Adjacent sequences: A110607 A110608 A110609 this_sequence A110611 A110612 A110613
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 30 2005
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