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A060453 Dot product of the squares and the quarter-squares: a(n) = sum(i=1..n, i^2 * floor(i^2/4)).

%I A060453 #20 Feb 28 2022 12:10:48
%S A060453 0,4,22,86,236,560,1148,2172,3792,6292,9922,15106,22204,31808,44408,
%T A060453 60792,81600,107844,140334,180334,228844,287408,357236,440180,537680,
%U A060453 651924,784602,938266,1114876,1317376,1548016,1810160,2106368,2440452
%N A060453 Dot product of the squares and the quarter-squares: a(n) = sum(i=1..n, i^2 * floor(i^2/4)).
%H A060453 N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/Exists.pdf">Fat Struts: Constructions and a Bound</a>, Proceedings Information Theory Workshop, Taormino, Italy, 2009. [<a href="/A047896/a047896.pdf">Cached copy</a>]
%H A060453 N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/FATS.pdf">A Note on Projecting the Cubic Lattice</a>, Discrete and Computational Geometry, Vol. 46 (No. 3, 2011), 472-478.
%H A060453 N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, <a href="http://neilsloane.com/doc/main_fat_strut.pdf">The Lifting Construction: A General Solution to the Fat Strut Problem</a>, Proceedings International Symposium on Information Theory (ISIT), 2010, IEEE Press. [<a href="/A047896/a047896_1.pdf">Cached copy</a>]
%H A060453 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-8,6,6,-8,0,3,-1).
%F A060453 G.f.: 2*x^2*(2+5*x+10*x^2+5*x^3+2*x^4)  / ( (1+x)^3*(x-1)^6 ). - _R. J. Mathar_, Apr 04 2012
%p A060453 See A060452.
%t A060453 A060453[n_]:=Sum[i^2*Floor[i^2/4],{i,1,n}]; Array[A060453,100] (* _Enrique Pérez Herrero_, Mar 19 2012 *)
%o A060453 (PARI) a(n)=sum(i=1,n,i^2\4*i^2) \\ _Charles R Greathouse IV_, Mar 20 2012
%Y A060453 Cf. A002620.
%K A060453 nonn,easy
%O A060453 1,2
%A A060453 _N. J. A. Sloane_ and Vinay Vaishampayan, Apr 09 2001