A162626 If 0 <= n <= 3 then a(n) = n(n+1)(n+2)/3, if n >= 4 then a(n) = n(n^2+5)/3.

0, 2, 8, 20, 28, 50, 82, 126, 184, 258, 350, 462, 596, 754, 938, 1150, 1392, 1666, 1974, 2318, 2700, 3122, 3586, 4094, 4648, 5250, 5902, 6606, 7364, 8178, 9050, 9982, 10976, 12034, 13158, 14350, 15612, 16946, 18354, 19838, 21400, 23042, 24766, 26574

Offset

0,2

Comments

One way to generalize the magic number sequence in A018226.

See also A130598 and A162630.

Links

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

Formula

From Daniel Forgues, May 03 2011: (Start)

If 0 <= n <= 3 then a(n) = 2 T_n, otherwise a(n) = 2 (T_n - t_{n-1}), where T_n is the n-th tetrahedral number, t_n the n-th triangular number.

G.f.: (2*x*(1 - 6*x^3 + 14*x^4 - 11*x^5 + 3*x^6))/(1 - x)^4, n >= 0.

(End)

a(n) = n*(n^2+5)/3 + (4*n-6)*A171386(n). - Omar E. Pol, Aug 14 2013

Crossrefs

Cf. A007290, A018226, A033547, A130598, A162518, A162519, A162521, A162522, A162523, A162524, A162525, A162630.

Sequence in context: A190640 A230434 A018226 * A137306 A110856 A048041

Adjacent sequences: A162623 A162624 A162625 * A162627 A162628 A162629

Keyword

easy,nonn

Author

Omar E. Pol, Jul 07 2009, Jul 13 2009

Extensions

Edited by N. J. A. Sloane, Jul 18 2009

Status

approved