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%I #20 Sep 08 2022 08:45:13
%S 0,4,76,344,936,1980,3604,5936,9104,13236,18460,24904,32696,41964,
%T 52836,65440,79904,96356,114924,135736,158920,184604,212916,243984,
%U 277936,314900,355004,398376,445144,495436,549380,607104,668736,734404,804236
%N Column 4 of A048790.
%D Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
%H Vincenzo Librandi, <a href="/A094160/b094160.txt">Table of n, a(n) for n = 1..1000</a>
%H R. C. Schroeppel, <a href="http://www.experimentalmath.info/workshop2004/schroeppel-talk.pdf">A few mathematical experiments</a>, Experimental Mathematics Workshop, Oakland, California, March 30, 2004.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A polynomial in n of degree 3.
%F a(n) = 64/3 n^3 - 30 n^2 + 38/3 n. - _Joshua Zucker_, Aug 14 2006
%F From _Colin Barker_, Aug 28 2016: (Start)
%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>4.
%F G.f.: 4*x^2*(1+15*x+16*x^2) / (1-x)^4.
%F (End)
%t Table[(64/3 n^3 - 30 n^2 + 38/3 n), {n, 0, 80}] (* _Vincenzo Librandi_, Aug 28 2016 *)
%o (Magma) [64/3*n^3-30*n^2+38/3*n: n in [0..60]]; // _Vincenzo Librandi_, Aug 28 2016
%o (PARI) concat(0, Vec(4*x^2*(1+15*x+16*x^2)/(1-x)^4 + O(x^60))) \\ _Colin Barker_, Aug 28 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, May 05 2004
%E More terms from _Joshua Zucker_, Aug 14 2006
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