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A139598 A035008(n) followed by A139098(n+1).

%I A139598 #27 Oct 01 2022 19:37:22
%S A139598 0,8,16,32,48,72,96,128,160,200,240,288,336,392,448,512,576,648,720,
%T A139598 800,880,968,1056,1152,1248,1352,1456,1568,1680,1800,1920,2048,2176,
%U A139598 2312,2448,2592,2736,2888,3040,3200,3360,3528,3696,3872
%N A139598 A035008(n) followed by A139098(n+1).
%C A139598 Sequence found by reading the line from 0, in the direction 0, 8, ... and the line from 16, in the direction 16, 48, ..., in the square spiral whose vertices are the triangular numbers A000217.
%C A139598 Also represents the minimum number of segments in the smooth Jordan curve which crosses every edge of an n X n square lattice exactly once. For example, the curve for a 3 X 3 lattice would have at least 32 segments. - _Nikolas Novakovic_, Aug 28 2022
%H A139598 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%H A139598 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A139598 Array read by rows: row n gives 8*n^2 + 8*n, 8*(n+1)^2.
%F A139598 From _Colin Barker_, Jul 22 2012: (Start)
%F A139598 a(n) = (1 - (-1)^n + 4*n + 2*n^2).
%F A139598 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A139598 G.f.: 8*x/((1-x)^3*(1+x)). (End)
%F A139598 a(n) = 8*A002620(n+1). - _R. J. Mathar_, May 04 2014
%e A139598 Array begins:
%e A139598    0,   8;
%e A139598   16,  32;
%e A139598   48,  72;
%e A139598   96, 128;
%t A139598 LinearRecurrence[{2,0,-2,1},{0,8,16,32},50] (* _Harvey P. Dale_, Sep 27 2019 *)
%Y A139598 Cf. A000217, A035008, A046092, A139098, A077221, A139591, A139592, A139593, A139595, A139596, A139597.
%K A139598 easy,nonn
%O A139598 0,2
%A A139598 _Omar E. Pol_, May 03 2008