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

0,2

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

Links

Table of n, a(n) for n=0..43.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A259751 A106841 A260711 * A137243 A360124 A303026

Adjacent sequences: A139595 A139596 A139597 * A139599 A139600 A139601

Keyword

easy,nonn

Author

Omar E. Pol, May 03 2008

Status

approved