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A174679 a(4n) = n^2. a(4n+1) = (4n-1)^2. a(4n+2) = (2n)^2. a(4n+3) = (4n+1)^2.

%I A174679 #36 Mar 16 2023 07:14:44
%S A174679 0,1,0,1,1,9,4,25,4,49,16,81,9,121,36,169,16,225,64,289,25,361,100,
%T A174679 441,36,529,144,625,49,729,196,841,64,961,256,1089,81,1225,324,1369,
%U A174679 100,1521,400,1681,121,1849,484,2025,144,2209,576
%N A174679 a(4n) = n^2. a(4n+1) = (4n-1)^2. a(4n+2) = (2n)^2. a(4n+3) = (4n+1)^2.
%H A174679 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
%F A174679 a(2n) = A174595(n).
%F A174679 a(2n+1) = A016754(n-1) = (2n-1)^2, n>0.
%F A174679 a(4n+1) = A016838(n-1).
%F A174679 a(4n+2) = A016742(n).
%F A174679 a(4n+3) = A016814(n).
%F A174679 a(n)= +3*a(n-4) -3*a(n-8) +a(n-12).
%F A174679 G.f.: -x*(1+x^2+x^3+6*x^4+4*x^5+22*x^6+x^7+25*x^8+4*x^9+9*x^10) / ( (x-1)^3*(1+x)^3*(x^2+1)^3 ). - _R. J. Mathar_, Dec 01 2010
%F A174679 a(n) = ((16-(1+(-1)^n)*(5+i^n))*n-4*(8-(1+(-1)^n)*(3+i^n)))^2/256, where i=sqrt(-1). - _Bruno Berselli_, Jan 27 2011 - Apr 09 2011
%t A174679 LinearRecurrence[{0,0,0,3,0,0,0,-3,0,0,0,1},{0,1,0,1,1,9,4,25,4,49,16,81},80] (* _Harvey P. Dale_, Apr 01 2018 *)
%K A174679 nonn,easy
%O A174679 0,6
%A A174679 _Paul Curtz_, Nov 30 2010