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A152745
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5 times hexagonal numbers: 5*n*(2*n-1).
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5
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0, 5, 30, 75, 140, 225, 330, 455, 600, 765, 950, 1155, 1380, 1625, 1890, 2175, 2480, 2805, 3150, 3515, 3900, 4305, 4730, 5175, 5640, 6125, 6630, 7155, 7700, 8265, 8850, 9455, 10080, 10725, 11390, 12075, 12780, 13505, 14250, 15015
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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, 5, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 18 2011
Also sequence found by reading the line from 0, in the direction 0, 5, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is one of the four semi-diagonals of the spiral. - Omar E. Pol, Oct 14 2011
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LINKS
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Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 10*n^2 - 5*n = A000384(n)*5.
a(n) = a(n-1) + 20*n-15 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
From G. C. Greubel, Sep 01 2018: (Start)
G.f.: 5*x*(1+ 3*x)/(1-x)^3.
E.g.f.: 5*x*(1+2*x)*exp(x). (End)
From Vaclav Kotesovec, Sep 02 2018: (Start)
Sum_{n>=1} 1/a(n) = 2*log(2)/5.
Sum_{n>=1} (-1)^n/a(n) = log(2)/5 - Pi/10. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {0, 5, 30}, 50] (* or *) Table[5*n*(2*n-1), {n, 0, 50}] (* G. C. Greubel, Sep 01 2018 *)
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PROG
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(PARI) a(n)=5*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017
(MAGMA) [5*n*(2*n-1): n in [0..50]]; // G. C. Greubel, Sep 01 2018
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CROSSREFS
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Cf. A000384, A085250, A152746.
Bisection of A028895.
Sequence in context: A043886 A044463 A270811 * A187275 A273480 A164015
Adjacent sequences: A152742 A152743 A152744 * A152746 A152747 A152748
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol, Dec 12 2008
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STATUS
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approved
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