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A060300
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a(n) = (2n(n+1))^2.
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10
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0, 16, 144, 576, 1600, 3600, 7056, 12544, 20736, 32400, 48400, 69696, 97344, 132496, 176400, 230400, 295936, 374544, 467856, 577600, 705600, 853776, 1024144, 1218816, 1440000, 1690000, 1971216, 2286144, 2637376, 3027600
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OFFSET
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0,2
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COMMENTS
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Arises from middle column of following triangle: 4^2, 12^2, 24^2,...:
....................... 3^2 + 4^2 = 5^2
............... 10^2 + 11^2 + 12^2 = 13^2 + 14^2
........ 21^2 + 22^2 + 23^2 + 24^2 = 25^2 + 26^2 + 27^2
. 36^2 + 37^2 + 38^2 + 39^2 + 40^2 = 41^2 + 42^2 + 43^2 + 44^2, etc.
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REFERENCES
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C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Oxford University Press, NY, 1966, pp. 90-92.
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LINKS
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FORMULA
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a(n) = Integral_{x=1..2*n+1} (x^3-x) dx. - César Aguilera, Jun 27 2020
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MATHEMATICA
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CoefficientList[Series[16 x (1 + 4 x + x^2) / (1 - x)^5, {x, 0, 33}], x] (* Vincenzo Librandi, Nov 18 2016 *)
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PROG
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(PARI) { for (n=0, 1000, write("b060300.txt", n, " ", (2*n*(n + 1))^2); ) } \\ Harry J. Smith, Jul 03 2009
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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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Corrected the definition from 2n(n+1)^2 to (2n(n+1))^2. - Harry J. Smith, Jul 03 2009
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STATUS
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approved
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