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%I M2776 #32 Sep 08 2022 08:44:35
%S 0,3,9,21,39,66,102,150,210,285,375,483,609,756,924,1116,1332,1575,
%T 1845,2145,2475,2838,3234,3666,4134,4641,5187,5775,6405,7080,7800,
%U 8568,9384,10251,11169,12141,13167,14250,15390,16590,17850,19173,20559,22011,23529,25116,26772,28500,30300
%N a(n) = floor(n*(n+2)*(2*n-1)/8).
%D From a problem on p. 151 of J. Rec. Math., 7 (1975).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. C. Greubel, <a href="/A007518/b007518.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -2, 3, -1).
%F a(n) = 3*A002623(n) for n>0. - _M. F. Hasler_, Sep 15 2009
%F G.f.: 3*x/((x+1)*(x-1)^4). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
%F 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
%p [seq(floor(n*(n+2)*(2*n-1)/8),n=1..50)]; # _Muniru A Asiru_, Mar 22 2018
%t 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 *)
%o (PARI) vector(50, n, n*(n+2)*(2*n-1)\8) \\ _Michel Marcus_, Oct 12 2014
%o (Magma) [Floor(n*(n+2)(2*n-1)/8): n in [1..50]]; // _G. C. Greubel_, Mar 21 2018
%o (GAP) List([1..50],n->Int(n*(n+2)*(2*n-1)/8)); # _Muniru A Asiru_, Mar 22 2018
%Y Column 4 of triangle A094953.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, _Robert G. Wilson v_
%E Offset corrected by _Harvey P. Dale_, Oct 06 2014
%E Terms a(40) onward added by _G. C. Greubel_, Mar 21 2018
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