This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173960 #12 Nov 01 2024 18:06:22
%S A173960 21,41,69,105,149,201,261,329,405,489,581,681,789,905,1029,1161,1301,
%T A173960 1449,1605,1769,1941,2121,2309,2505,2709,2921,3141,3369,3605,3849,
%U A173960 4101,4361,4629,4905,5189,5481,5781,6089,6405,6729,7061,7401,7749,8105,8469
%N A173960 Averages of four consecutive odd squares.
%C A173960 The averages of four consecutive even squares are in A027575.
%H A173960 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A173960 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 A173960 From _Colin Barker_, Apr 15 2012: (Start)
%F A173960 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A173960 G.f.: x*(21-22*x+9*x^2)/(1-x)^3. (End)
%F A173960 E.g.f.: exp(x)*(4*x^2 + 12*x + 9) - 9. - _Elmo R. Oliveira_, Nov 01 2024
%e A173960 (1^2 + 3^2 + 5^2 + 7^2)/4 = 21.
%p A173960 A173960 := proc(n) 4*n^2+8*n+9 ; end proc: seq(A173960(n),n=1..100) ; # _R. J. Mathar_, Mar 31 2010
%t A173960 f[n_]:=(n^2+(n+2)^2+(n+4)^2+(n+6)^2)/4;Table[f[n],{n,1,6!,2}]
%o A173960 (PARI) a(n)=4*n^2+8*n+9 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A173960 Cf. A027575.
%K A173960 nonn,easy
%O A173960 1,1
%A A173960 _Vladimir Joseph Stephan Orlovsky_, Mar 03 2010
%E A173960 Formula corrected by _R. J. Mathar_, Mar 31 2010