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

0,2

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

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

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

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

Sequence in context: A240371 A158653 A129215 * A121471 A293766 A178946

Adjacent sequences: A139590 A139591 A139592 * A139594 A139595 A139596

Keyword

easy,nonn

Author

Omar E. Pol, May 03 2008

Extensions

Edited by Omar E. Pol, Jul 13 2009

Status

approved