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%I #8 Jun 17 2017 03:23:50
%S 21,41,69,105,149,201,261,329,405,489,581,681,789,905,1029,1161,1301,
%T 1449,1605,1769,1941,2121,2309,2505,2709,2921,3141,3369,3605,3849,
%U 4101,4361,4629,4905,5189,5481,5781,6089,6405,6729,7061,7401,7749,8105,8469
%N Averages of four consecutive odd squares.
%C The averages of four consecutive even squares are in A027575.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F 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.
%F 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. - _Colin Barker_, Apr 15 2012
%e (1^2 + 3^2 + 5^2 + 7^2)/4 = 21.
%p A173960 := proc(n) 4*n^2+8*n+9 ; end proc: seq(A173960(n),n=1..100) ; # _R. J. Mathar_, Mar 31 2010
%t f[n_]:=(n^2+(n+2)^2+(n+4)^2+(n+6)^2)/4;Table[f[n],{n,1,6!,2}]
%o (PARI) a(n)=4*n^2+8*n+9 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A027575.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 03 2010
%E Formula corrected by _R. J. Mathar_, Mar 31 2010
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