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

1,3

Links

Table of n, a(n) for n=1..50.

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).

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

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;

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 *)

Crossrefs

Cf. A002620, A000538, A059859. Agrees with A060453 for first 37 terms.

Sequence in context: A360739 A352305 A060454 * A229620 A045949 A189492

Adjacent sequences: A060449 A060450 A060451 * A060453 A060454 A060455

Keyword

nonn

Author

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

Status

approved