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A014635
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a(n) = 2*n*(4*n - 1).
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20
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0, 6, 28, 66, 120, 190, 276, 378, 496, 630, 780, 946, 1128, 1326, 1540, 1770, 2016, 2278, 2556, 2850, 3160, 3486, 3828, 4186, 4560, 4950, 5356, 5778, 6216, 6670, 7140, 7626, 8128, 8646, 9180, 9730, 10296, 10878, 11476, 12090, 12720, 13366, 14028, 14706
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OFFSET
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0,2
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COMMENTS
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Even hexagonal numbers.
Number of edges in the join of two complete graphs of order 3n and n, K_3n * K_n - Roberto E. Martinez II, Jan 07 2002
Bisection of A000384. Also, this sequence arises from reading the line from 0, in the direction 0, 6, ..., in the square spiral whose vertices are the triangular numbers A000217. Perfect numbers are members of this sequence because a(A134708(n)) = A000396(n). Also, positive members are a bisection of A139596. - Omar E. Pol, May 07 2008
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = 3*log(2)/2 - Pi/4.
Sum_{n>=1} (-1)^n / a(n) = log(2)/2 + log(1+sqrt(2))/sqrt(2) - Pi / 2^(3/2). (End)
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MAPLE
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MATHEMATICA
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Table[2*n*(4*n - 1), {n, 0, 50}] (* G. C. Greubel, Jul 18 2017 *)
PolygonalNumber[6, Range[0, 90, 2]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 6, 28}, 50] (* Harvey P. Dale, Jan 21 2023 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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