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

Author

Omar E. Pol, May 03 2008

Keywords

• easy
• nonn

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.

Examples

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

Links

• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

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

Programs

Mathematica

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

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