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
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
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, May 03 2008
STATUS
approved