OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).
FORMULA
a(n) = 2a(n-1)+2a(n-2)-6a(n-3)+6a(n-5)-2a(n-6)-2a(n-7)+a(n-8).
From Alois P. Heinz, May 31 2012: (Start)
a(n) = A006578(n)^2.
G.f.: x*(14*x+30*x^2+42*x^3+17*x^4+4*x^5+1) / ((x+1)^3*(1-x)^5). (End)
MAPLE
a:= n-> (n*(n+1)/2+floor(n^2/4))^2:
seq(a(n), n=0..60); # Alois P. Heinz, May 31 2012
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w <= 2 x && y <= 2 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212506 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 19 2012
STATUS
approved