A060452 Let v = (1,4,9,...,n^2), x = (0,1,2,4,6,...) [first n terms of A002620]; a(n) = v.v * x.x - (v.x)^2.
0, 1, 6, 38, 107, 350, 728, 1752, 3090, 6215, 9878, 17654, 26117, 42924, 60256, 93024, 125460, 184509, 241110, 341110, 434511, 595562, 742808, 991640, 1215110, 1586403, 1914822, 2452646, 2922185, 3681560, 4337024, 5385600, 6281704, 7701561, 8904294, 10793862, 12381939, 14858038, 16924440, 20124440, 22778042, 26862143, 30229430, 35383062, 39609933, 46046276, 51299936, 59262560, 65733500, 75499125
Offset: 1
Keywords
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 (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
Programs
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Maple
fv := n->1/30*n*(1+n)*(2*n+1)*(3*n^2+3*n-1); # this is A000538 f1 := n->1/160*(n-1)*(1+n)*(2*n^3+5*n^2+2*n-5); f2 := n->1/160*n*(n+2)*(2*n^3+n^2-2*n+4); f7 := n->if n mod 2 = 0 then f2(n) else f1(n) end if; # this is A059859 f3 := n->1/20*n^5+1/8*n^4+1/24*n^3-11/120*n-1/8*n^2; f4 := n->1/20*n^5+1/8*n^4+1/24*n^3+1/30*n; f5:-n-> if `mod`(n,2) = 0 then f4(n) else f3(n) end if; # this is A060453 A060452 := n->f7(n)*fv(n)-f5(n)^2;
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Mathematica
Table[Module[{nn=n,v,x},v=Range[nn]^2;x=Floor[v/4];v.v x.x-(v.x)^2],{n,50}] (* or *) LinearRecurrence[{1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1},{0,1,6,38,107,350,728,1752,3090,6215,9878,17654,26117},50] (* Harvey P. Dale, Aug 10 2021 *)
Formula
G.f. -x^2*(1+5*x+26*x^2+39*x^3+66*x^4+39*x^5+26*x^6+5*x^7+x^8) / ( (1+x)^6*(x-1)^7 ). - R. J. Mathar, Apr 04 2012