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A033537
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a(n) = n*(2*n+5).
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24
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0, 7, 18, 33, 52, 75, 102, 133, 168, 207, 250, 297, 348, 403, 462, 525, 592, 663, 738, 817, 900, 987, 1078, 1173, 1272, 1375, 1482, 1593, 1708, 1827, 1950, 2077, 2208, 2343, 2482, 2625, 2772, 2923, 3078, 3237, 3400, 3567, 3738, 3913, 4092, 4275, 4462, 4653, 4848, 5047, 5250, 5457, 5668
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OFFSET
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0,2
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COMMENTS
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Permutations avoiding 12-3 that contain the pattern 32-1 exactly once.
If Y is a 3-subset of an (2n+1)-set X then, for n>=1, a(n-1) is the number of (2n-1)-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007
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LINKS
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FORMULA
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G.f.: x*(7-3*x)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=7, a(2)=18. (End)
Sum_{n>=1} 1/a(n) = 46/75 - 2*log(2)/5.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/10 + log(2)/5 - 26/75. (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 7, 18}, 60] (* Harvey P. Dale, Nov 19 2021 *)
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PROG
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(GAP) List([0..60], n-> n*(2*n+5) ); # G. C. Greubel, Oct 14 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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