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A139267
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Twice octagonal numbers: 2*n*(3*n-2).
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12
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0, 2, 16, 42, 80, 130, 192, 266, 352, 450, 560, 682, 816, 962, 1120, 1290, 1472, 1666, 1872, 2090, 2320, 2562, 2816, 3082, 3360, 3650, 3952, 4266, 4592, 4930, 5280, 5642, 6016, 6402, 6800, 7210, 7632, 8066, 8512, 8970, 9440, 9922
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the line from 0, in the direction 0, 2,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A033580 in the same spiral. - Omar E. Pol, Sep 09 2011
After 0, a(n) = Sum_{i=0..n-1} (12*i + 2). - Bruno Berselli, Sep 11 2013
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LINKS
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FORMULA
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a(n) = 2*A000567(n) = 6*n^2 - 4*n = 2*n*(3*n - 2).
G.f.: x*(2+10*x)/(1-3*x+3*x^2-x^3). - Colin Barker, Jan 06 2012
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [2*n*(3*n-2): n in [0..50]]; // G. C. Greubel, Sep 18 2019
(Sage) [2*n*(3*n-2) for n in (0..50)] # G. C. Greubel, Sep 18 2019
(GAP) List([0..50], n-> 2*n*(3*n-2)); # G. C. Greubel, Sep 18 2019
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CROSSREFS
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Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this sequence is the case k=12).
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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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