OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 3, ... and the same line from 0, in the direction 0, 11, ..., in the square spiral whose vertices are the triangular numbers A000217.
A139593 appears (both numerically and via back of an envelope algebra, but not a publishable proof) to be the cumulative sum of A047470. - Markus J. Q. Roberts, Jul 12 2009
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 + 3n, 8*(n+1)^2 - 5(n+1).
From Colin Barker, Sep 15 2013: (Start)
a(n) = (-1 + (-1)^n + 6*n + 8*n^2)/4.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: -x*(5*x+3) / ((x-1)^3*(x+1)). (End)
EXAMPLE
Array begins:
0, 3;
11, 22;
38, 57;
81, 108;
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1}, {0, 3, 11, 22}, 50] (* Harvey P. Dale, Feb 09 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, May 03 2008
EXTENSIONS
Edited by Omar E. Pol, Jul 13 2009
STATUS
approved