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 A007518 Floor(n*(n+2)*(2*n-1)/8). (Formerly M2776) 2

%I M2776

%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

%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 <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(1)=0, a(2)=3, a(3)=9, a(4)=21, a(5)=39, a(n)=3*a(n-1)-2*a(n-2)- 2*a(n-3)+ 3*a(n-4)-a (n-5). - _Harvey P. Dale_, Oct 06 2014

%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

%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

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