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A152744
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7 times pentagonal numbers: a(n) = 7*n*(3*n-1)/2.
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4
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0, 7, 35, 84, 154, 245, 357, 490, 644, 819, 1015, 1232, 1470, 1729, 2009, 2310, 2632, 2975, 3339, 3724, 4130, 4557, 5005, 5474, 5964, 6475, 7007, 7560, 8134, 8729, 9345, 9982, 10640, 11319, 12019, 12740, 13482, 14245, 15029, 15834, 16660, 17507, 18375, 19264
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (21*n^2 - 7*n)/2 = A000326(n)*7.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Harvey P. Dale, Aug 08 2013
a(n) = Sum_{i = 2..8} P(i,n), where P(i,m) = m*((i-2)*m-(i-4))/2. - Bruno Berselli, Jul 04 2018
Sum_{n>=1} 1/a(n) = (9*log(3) - sqrt(3)*Pi)/21.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(Pi*sqrt(3) - 6*log(2))/21. (End)
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MATHEMATICA
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Table[7n (3n-1)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 7, 35}, 50] (* Harvey P. Dale, Aug 08 2013 *)
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PROG
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(Magma) [7*n*(3*n-1)/2: n in [0..50]]; // G. C. Greubel, Sep 01 2018
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CROSSREFS
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Similar sequences are listed in A316466.
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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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