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A033486
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a(n) = n*(n + 1)*(n + 2)*(n + 3)/2.
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6
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0, 12, 60, 180, 420, 840, 1512, 2520, 3960, 5940, 8580, 12012, 16380, 21840, 28560, 36720, 46512, 58140, 71820, 87780, 106260, 127512, 151800, 179400, 210600, 245700, 285012, 328860, 377580, 431520, 491040, 556512, 628320, 706860, 792540, 885780, 987012
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OFFSET
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0,2
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COMMENTS
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a(n) is the area of an irregular quadrilateral with vertices at (1,1), (n+1, n+2), ((n+1)^2, (n+2)^2) and ((n+1)^3, (n+2)^3). - Art Baker, Dec 08 2018
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) with a(0) = 0, a(1) = 12, a(2) = 60, a(3) = 180, a(4) = 420. - Harvey P. Dale, Feb 04 2015
Sum_{n>=1} 1/a(n) = 1/9.
Sum_{n>=1} (-1)^(n+1)/a(n) = 8*(3*log(2)-2)/9. (End)
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MAPLE
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MATHEMATICA
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Table[n*(n + 1)*(n + 2)*(n + 3)/2, {n, 0, 50}] (* David Nacin, Mar 01 2012 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 12, 60, 180, 420}, 40] (* Harvey P. Dale, Feb 04 2015 *)
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PROG
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(GAP) List([0..40], n->n*(n+1)*(n+2)*(n+3)/2); # Muniru A Asiru, Dec 08 2018
(Sage) [12*binomial(n+3, 4) for n in range(40)] # G. C. Greubel, Dec 08 2018
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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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