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A174994 Repeat (8*n+4)^2.

%I A174994 #22 Jul 23 2025 23:11:37
%S A174994 16,16,144,144,400,400,784,784,1296,1296,1936,1936,2704,2704,3600,
%T A174994 3600,4624,4624,5776,5776,7056,7056,8464,8464,10000,10000,11664,11664,
%U A174994 13456,13456,15376,15376,17424,17424,19600,19600,21904,21904,24336,24336,26896,26896,29584,29584,32400,32400,35344,35344
%N A174994 Repeat (8*n+4)^2.
%H A174994 Colin Barker, <a href="/A174994/b174994.txt">Table of n, a(n) for n = 0..1000</a>
%H A174994 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A174994 a(n) = A174683(A043547(n+1)).
%F A174994 a(2n) = a(2n+1) = A017114(n).
%F A174994 From _R. J. Mathar_, Dec 02 2010: (Start)
%F A174994 a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).
%F A174994 G.f.: ( -16-96*x^2-16*x^4 ) / ( (1+x)^2*(x-1)^3 ). (End)
%F A174994 From _Colin Barker_, Jan 26 2016: (Start)
%F A174994 a(n) = 8*(2*n^2+2*(-1)^n*n+2*n+(-1)^n+1).
%F A174994 a(n) = 16*n^2+32*n+16 for n even.
%F A174994 a(n) = 16*n^2 for n odd. (End)
%F A174994 a(n) = (8*floor(n/2)+4)^2. - _Bruno Berselli_, Jan 26 2016
%t A174994 (8*Floor[Range[0, 50]/2] + 4)^2 (* _Wesley Ivan Hurt_, Jul 23 2025 *)
%o A174994 (PARI) Vec((-16-96*x^2-16*x^4)/((1+x)^2*(x-1)^3) + O(x^100)) \\ _Colin Barker_, Jan 26 2016
%Y A174994 Cf. A017114, A043547, A174683.
%K A174994 nonn,less,easy
%O A174994 0,1
%A A174994 _Paul Curtz_, Dec 02 2010