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A099761
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a(n) = ( n*(n+2) )^2.
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6
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0, 9, 64, 225, 576, 1225, 2304, 3969, 6400, 9801, 14400, 20449, 28224, 38025, 50176, 65025, 82944, 104329, 129600, 159201, 193600, 233289, 278784, 330625, 389376, 455625, 529984, 613089, 705600, 808201, 921600, 1046529, 1183744, 1334025
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OFFSET
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0,2
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COMMENTS
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Using four consecutive triangular numbers t1, t2, t3, t4, form a 2 X 2 determinant with the first row t1 and t2 and the second row t3 and t4. Squaring the determinant gives the numbers in this sequence. - J. M. Bergot, May 17 2012
Numbers k such that sqrt(1 + sqrt(k)) is integer. - Jaroslav Krizek, Jan 23 2014
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LINKS
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FORMULA
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G.f.: x*(9 +19*x -5*x^2 +x^3)/(1-x)^5. - R. J. Mathar, Apr 02 2011
E.g.f.: exp(x)*x*(9 + 23*x + 10*x^2 + x^3). - Stefano Spezia, Aug 05 2019
Sum_{n>=1} 1/a(n) = Pi^2/12 - 11/16.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/24 - 5/16. (End)
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MAPLE
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A099761 := proc(n) n^2*(n+2)^2 ; end proc:
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MATHEMATICA
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PROG
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(Magma) [(n*(n+2))^2: n in [0..40]]; // G. C. Greubel, Sep 03 2019
(Sage) [(n*(n+2))^2 for n in (0..40)] # G. C. Greubel, Sep 03 2019
(GAP) List([0..40], n-> (n*(n+2))^2); # G. C. Greubel, Sep 03 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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Kari Lajunen (Kari.Lajunen(AT)Welho.com), Nov 11 2004
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EXTENSIONS
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Deleted a trivial formula which was based on another offset - R. J. Mathar, Dec 16 2009
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STATUS
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approved
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