A139593 A139276(n) followed by A139272(n+1).

0, 3, 11, 22, 38, 57, 81, 108, 140, 175, 215, 258, 306, 357, 413, 472, 536, 603, 675, 750, 830, 913, 1001, 1092, 1188, 1287, 1391, 1498, 1610, 1725, 1845, 1968, 2096, 2227, 2363, 2502, 2646, 2793, 2945, 3100, 3260, 3423, 3591, 3762

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, 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

Examples

			Array begins:
   0,   3;
  11,  22;
  38,  57;
  81, 108;
		

Links

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

Crossrefs

Cf. A000217, A046092, A139272, A139276, A077221, A139591, A139592, A139594, A139595, A139596, A139597, A139598, A047470.

Programs

Mathematica

LinearRecurrence[{2,0,-2,1},{0,3,11,22},50] (* Harvey P. Dale, Feb 09 2019 *)

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)

Extensions

Edited by Omar E. Pol, Jul 13 2009