A139596 A033587(n) followed by even hexagonal number A014635(n+1).

0, 6, 14, 28, 44, 66, 90, 120, 152, 190, 230, 276, 324, 378, 434, 496, 560, 630, 702, 780, 860, 946, 1034, 1128, 1224, 1326, 1430, 1540, 1652, 1770, 1890, 2016, 2144, 2278, 2414, 2556, 2700, 2850, 3002, 3160, 3320, 3486, 3654, 3828

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 6,... and the same line from 0, in the direction 0, 14,..., in the square spiral whose vertices are the triangular numbers A000217.

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 + 6*n, 8*(n+1)^2 - 2(n+1).

O.g.f.: -2*x*(x+3)/((x-1)^3*(1+x)). - R. J. Mathar, May 06 2008

a(n) = 2*A156859(n). - R. J. Mathar, Feb 28 2018

Example

Array begins:
0, 6
14, 28
44, 66
90, 120

Mathematica

LinearRecurrence[{2, 0, -2, 1}, {0, 6, 14, 28}, 50] (* Harvey P. Dale, Jan 20 2024 *)

Crossrefs

Cf. A000217, A014635, A033587, A046092, A077221, A139591, A139592, A139593, A139595, A139597, A139598.

Sequence in context: A349723 A378230 A128806 * A192035 A345332 A183023

Adjacent sequences: A139593 A139594 A139595 * A139597 A139598 A139599

Keyword

easy,nonn

Author

Omar E. Pol, May 03 2008

Status

approved