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A173960 Averages of four consecutive odd squares. 5

%I

%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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Last modified November 16 19:17 EST 2019. Contains 329201 sequences. (Running on oeis4.)