A152751 3 times octagonal numbers: a(n) = 3*n*(3*n-2).
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, 14160, 14883, 15624, 16383, 17160
Offset: 0
Examples
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)
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Programs
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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 *) -
PARI
a(n)=3*n*(3*n-2) \\ Charles R Greathouse IV, Sep 24 2015
Formula
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
From Elmo R. Oliveira, Dec 25 2024: (Start)
E.g.f.: 3*exp(x)*x*(1 + 3*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3.
a(n) = n + A152995(n). (End)
Comments