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A007518
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a(n) = floor(n*(n+2)*(2*n-1)/8).
(Formerly M2776)
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3
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0, 3, 9, 21, 39, 66, 102, 150, 210, 285, 375, 483, 609, 756, 924, 1116, 1332, 1575, 1845, 2145, 2475, 2838, 3234, 3666, 4134, 4641, 5187, 5775, 6405, 7080, 7800, 8568, 9384, 10251, 11169, 12141, 13167, 14250, 15390, 16590, 17850, 19173, 20559, 22011, 23529, 25116, 26772, 28500, 30300
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OFFSET
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1,2
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REFERENCES
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From a problem on p. 151 of J. Rec. Math., 7 (1975).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: 3*x/((x+1)*(x-1)^4). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5) with a(1)=0, a(2)=3, a(3)=9, a(4)=21, a(5)=39. - Harvey P. Dale, Oct 06 2014
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MAPLE
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[seq(floor(n*(n+2)*(2*n-1)/8), n=1..50)]; # Muniru A Asiru, Mar 22 2018
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MATHEMATICA
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Table[Floor[(n(n+2)(2n-1))/8], {n, 50}] (* or *) LinearRecurrence[{3, -2, -2, 3, -1}, {0, 3, 9, 21, 39}, 40] (* Harvey P. Dale, Oct 06 2014 *)
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PROG
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(PARI) vector(50, n, n*(n+2)*(2*n-1)\8) \\ Michel Marcus, Oct 12 2014
(Magma) [Floor(n*(n+2)(2*n-1)/8): n in [1..50]]; // G. C. Greubel, Mar 21 2018
(GAP) List([1..50], n->Int(n*(n+2)*(2*n-1)/8)); # Muniru A Asiru, Mar 22 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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EXTENSIONS
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STATUS
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approved
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