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A035008(n) followed by A139098(n+1).
8

%I #27 Oct 01 2022 19:37:22

%S 0,8,16,32,48,72,96,128,160,200,240,288,336,392,448,512,576,648,720,

%T 800,880,968,1056,1152,1248,1352,1456,1568,1680,1800,1920,2048,2176,

%U 2312,2448,2592,2736,2888,3040,3200,3360,3528,3696,3872

%N A035008(n) followed by A139098(n+1).

%C 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 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 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F Array read by rows: row n gives 8*n^2 + 8*n, 8*(n+1)^2.

%F From _Colin Barker_, Jul 22 2012: (Start)

%F a(n) = (1 - (-1)^n + 4*n + 2*n^2).

%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

%F G.f.: 8*x/((1-x)^3*(1+x)). (End)

%F a(n) = 8*A002620(n+1). - _R. J. Mathar_, May 04 2014

%e Array begins:

%e 0, 8;

%e 16, 32;

%e 48, 72;

%e 96, 128;

%t LinearRecurrence[{2,0,-2,1},{0,8,16,32},50] (* _Harvey P. Dale_, Sep 27 2019 *)

%Y Cf. A000217, A035008, A046092, A139098, A077221, A139591, A139592, A139593, A139595, A139596, A139597.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, May 03 2008