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

0, 4, 22, 86, 236, 560, 1148, 2172, 3792, 6292, 9922, 15106, 22204, 31808, 44408, 60792, 81600, 107844, 140334, 180334, 228844, 287408, 357236, 440180, 537680, 651924, 784602, 938266, 1114876, 1317376, 1548016, 1810160, 2106368, 2440452

Offset: 1

Author

N. J. A. Sloane and Vinay Vaishampayan, Apr 09 2001

Keywords

• nonn
• easy

Links

• N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, Fat Struts: Constructions and a Bound, Proceedings Information Theory Workshop, Taormino, Italy, 2009. [Cached copy]
• N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, A Note on Projecting the Cubic Lattice, Discrete and Computational Geometry, Vol. 46 (No. 3, 2011), 472-478.
• N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, The Lifting Construction: A General Solution to the Fat Strut Problem, Proceedings International Symposium on Information Theory (ISIT), 2010, IEEE Press. [Cached copy]
• Index entries for linear recurrences with constant coefficients, signature (3,0,-8,6,6,-8,0,3,-1).

Crossrefs

Cf. A002620.

Programs

Maple

See A060452.

Mathematica

A060453[n_]:=Sum[i^2*Floor[i^2/4],{i,1,n}]; Array[A060453,100] (* Enrique Pérez Herrero, Mar 19 2012 *)

PARI

a(n)=sum(i=1,n,i^2\4*i^2) \\ Charles R Greathouse IV, Mar 20 2012

Formula

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