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

0, 8, 16, 32, 48, 72, 96, 128, 160, 200, 240, 288, 336, 392, 448, 512, 576, 648, 720, 800, 880, 968, 1056, 1152, 1248, 1352, 1456, 1568, 1680, 1800, 1920, 2048, 2176, 2312, 2448, 2592, 2736, 2888, 3040, 3200, 3360, 3528, 3696, 3872

Offset: 0

Author

Omar E. Pol, May 03 2008

Keywords

• easy
• nonn

Comments

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.

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

Examples

			Array begins:
   0,   8;
  16,  32;
  48,  72;
  96, 128;
		

Links

• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{2,0,-2,1},{0,8,16,32},50] (* Harvey P. Dale, Sep 27 2019 *)

Formula

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

From Colin Barker, Jul 22 2012: (Start)

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

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

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

a(n) = 8*A002620(n+1). - R. J. Mathar, May 04 2014