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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.
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.
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
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