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A152751
3 times octagonal numbers: a(n) = 3*n*(3*n-2).
20
0, 3, 24, 63, 120, 195, 288, 399, 528, 675, 840, 1023, 1224, 1443, 1680, 1935, 2208, 2499, 2808, 3135, 3480, 3843, 4224, 4623, 5040, 5475, 5928, 6399, 6888, 7395, 7920, 8463, 9024, 9603, 10200, 10815, 11448, 12099, 12768, 13455
OFFSET
0,2
COMMENTS
a(n) also can be represented as n concentric triangles (see example). - Omar E. Pol, Aug 21 2011
FORMULA
a(n) = 9*n^2 - 6*n = A000567(n)*3 = A064201(n)/3.
a(n) = a(n-1) + 18*n - 15 with n>0, a(0)=0. - Vincenzo Librandi, Nov 26 2010
G.f.: 3*x*(1+5*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011
EXAMPLE
From Omar E. Pol, Aug 21 2011: (Start)
Illustration of initial terms as concentric triangles:
.
. o
. o o
. o o
. o o
. o o o o
. o o o o o o
. o o o o o o
. o o o o o o
. o o o o o o o o o
. o o o o o o o o o o o o
. o o o o o o
. o o o o o o o o o o o o o o o o o o
. o o
. o o o o o o o o o o o o o o
.
. 3 24 63
(End)
MATHEMATICA
s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 6!, 18}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
3*PolygonalNumber[8, Range[0, 40]] (* Harvey P. Dale, May 08 2022 *)
PROG
(PARI) a(n)=3*n*(3*n-2) \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A033581, A085250, A152734, A194273. - Omar E. Pol, Aug 21 2011
Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=18: see Comments lines of A226492.
Sequence in context: A101008 A070734 A009113 * A369953 A162654 A092468
KEYWORD
easy,nonn,changed
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved