OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-8,6,6,-8,0,3,-1).
FORMULA
If n is even, a(n) = n*(n+2)*(2*n^3+n^2-2*n+4)/160; if n is odd, a(n) = (n^2-1)*(2*n^3+5*n^2+2*n-5)/160.
From R. J. Mathar, Feb 15 2010: (Start)
a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).
G.f.: x^2*(1+2*x+6*x^2+2*x^3+x^4) / ((1+x)^3*(x-1)^6). (End)
a(n) = Sum_{i=1..n} floor(i^2/4)^2. - Enrique Pérez Herrero, Mar 20 2012
a(n) = (2*n*(2*n^4+5*n^3-5*n+3) + 5*(2*n*(n+1)-1)*(-1)^n + 5)/320. - Bruno Berselli, Mar 21 2012
MAPLE
MATHEMATICA
a[n_] := Sum[Floor[i^2/4]^2, {i, 1, n}]; Table[a[n], {n, 0, 100}] (* Enrique Pérez Herrero, Mar 20 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 26 2001
STATUS
approved