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A033580
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Four times second pentagonal numbers: a(n) = 2*n*(3*n+1).
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12
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0, 8, 28, 60, 104, 160, 228, 308, 400, 504, 620, 748, 888, 1040, 1204, 1380, 1568, 1768, 1980, 2204, 2440, 2688, 2948, 3220, 3504, 3800, 4108, 4428, 4760, 5104, 5460, 5828, 6208, 6600, 7004, 7420, 7848, 8288, 8740, 9204, 9680, 10168, 10668, 11180, 11704, 12240
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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, 8,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A139267 in the same spiral - Omar E. Pol, Sep 09 2011
a(n) is the number of edges of the octagonal network O(n,n); O(m,n) is defined by Fig. 1 of the Siddiqui et al. reference. - Emeric Deutsch May 13 2018
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = 3/2 - Pi/(4*sqrt(3)) - 3*log(3)/4.
Sum_{n>=1} (-1)^(n+1)/a(n) = -3/2 + Pi/(2*sqrt(3)) + log(2). (End)
a(n) = 4*A005449(n). See Four Quarter Star Crosses illustration.
a(n) = A046092(n-1) + A033996(n). See Triangulated Star Crosses illustration.
a(n) = 4*A000217(n-1) + 4*A002378. See Oblong Star Crosses illustration.
a(n) = A016754(n) + 4*A000217(n). See Crossed Diamond Stars illustration.
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [2*n*(3*n+1): n in [0..50]]; // G. C. Greubel, Oct 09 2019
(Sage) [2*n*(3*n+1) for n in (0..50)] # G. C. Greubel, Oct 09 2019
(GAP) List([0..50], n-> 2*n*(3*n+1)); # G. C. Greubel, Oct 09 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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