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A153808
8 times octagonal numbers: 8*n*(3*n-2).
3
0, 8, 64, 168, 320, 520, 768, 1064, 1408, 1800, 2240, 2728, 3264, 3848, 4480, 5160, 5888, 6664, 7488, 8360, 9280, 10248, 11264, 12328, 13440, 14600, 15808, 17064, 18368, 19720, 21120, 22568, 24064, 25608, 27200, 28840, 30528, 32264
OFFSET
0,2
FORMULA
a(n) = 24*n^2 - 16*n = 8*A000567(n) = 4*A139267(n) = 2*A153794(n).
a(n) = a(n-1) + 48*n - 40 (with a(0)=0). - Vincenzo Librandi, Nov 27 2010
From G. C. Greubel, Aug 29 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 8*x*(1 + 5*x)/(1 - x)^3.
E.g.f.: 8*x*(1 + 3*x)*exp(x). (End)
MATHEMATICA
Table[8*n*(3*n-2), {n, 0, 25}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 8, 64}, 25] (* G. C. Greubel, Aug 29 2016 *)
8*PolygonalNumber[8, Range[0, 40]] (* Harvey P. Dale, Nov 22 2023 *)
PROG
(Magma) [ 8*n*(3*n-2): n in [0..40] ];
(PARI) a(n)=24*n^2-16*n \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A000567 (octagonal numbers), A064201 (9 times octagonal numbers), A139267 (twice octagonal numbers), A152751 (3 times octagonal numbers), A153794 (4 times octagonal numbers).
Sequence in context: A255932 A043152 A044195 * A207601 A207027 A207172
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jan 19 2009
STATUS
approved