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A110611
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Minimal 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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1
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1, 4, 11, 21, 37, 58, 87, 123, 169, 224, 291, 369, 461, 566, 687, 823, 977, 1148, 1339, 1549, 1781, 2034, 2311, 2611, 2937, 3288, 3667, 4073, 4509, 4974, 5471, 5999, 6561, 7156, 7787, 8453, 9157, 9898, 10679, 11499, 12361, 13264, 14211, 15201, 16237
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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.
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FORMULA
| a(n)=(n^3+3*n^2+5*n-6)/6 if n is even; a(n)=(n^3+3*n^2+5*n-3)/6 if n is odd.
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EXAMPLE
| a(4)=21 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
| a:=proc(n) if n mod 2 = 0 then (n^3+3*n^2+5*n-6)/6 else (n^3+3*n^2+5*n-3)/6 fi end: seq(a(n), n=1..52);
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CROSSREFS
| Cf. A064842, A110610.
Sequence in context: A008017 A008205 A008095 * A008004 A009900 A008230
Adjacent sequences: A110608 A110609 A110610 * A110612 A110613 A110614
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 30 2005
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