OFFSET
1,1
COMMENTS
The averages of four consecutive even squares are in A027575.
LINKS
FORMULA
a(n) = ((2*n-1)^2 + (2*n+1)^2 + (2*n+3)^2 + (2*n+5)^2)/4 = 4*n^2 + 8*n + 9.
From Colin Barker, Apr 15 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(21-22*x+9*x^2)/(1-x)^3. (End)
E.g.f.: exp(x)*(4*x^2 + 12*x + 9) - 9. - Elmo R. Oliveira, Nov 01 2024
EXAMPLE
(1^2 + 3^2 + 5^2 + 7^2)/4 = 21.
MAPLE
MATHEMATICA
f[n_]:=(n^2+(n+2)^2+(n+4)^2+(n+6)^2)/4; Table[f[n], {n, 1, 6!, 2}]
PROG
(PARI) a(n)=4*n^2+8*n+9 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Vladimir Joseph Stephan Orlovsky, Mar 03 2010
EXTENSIONS
Formula corrected by R. J. Mathar, Mar 31 2010
STATUS
approved