A152759 3 times 9-gonal (or nonagonal) numbers: a(n) = 3*n*(7*n-5)/2.

0, 3, 27, 72, 138, 225, 333, 462, 612, 783, 975, 1188, 1422, 1677, 1953, 2250, 2568, 2907, 3267, 3648, 4050, 4473, 4917, 5382, 5868, 6375, 6903, 7452, 8022, 8613, 9225, 9858, 10512, 11187, 11883, 12600, 13338, 14097, 14877, 15678, 16500, 17343, 18207, 19092, 19998

Offset: 0

Author

Omar E. Pol, Dec 14 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001106, A139268, A226491.

3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152767, A153783, A153448, A153875.

Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=21: see Comments lines of A226492.

Programs

Mathematica

s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,3,6!,21}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
CoefficientList[Series[3 x (1 + 6 x) / (1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Jun 05 2013 *)
LinearRecurrence[{3,-3,1},{0,3,27},40] (* Harvey P. Dale, May 26 2015 *)

PARI

a(n)=3*n*(7*n-5)/2 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = (21*n^2 - 15*n)/2 = 3*A001106(n).

a(n) = a(n-1) + 21*n - 18 with n > 0, a(0)=0. - Vincenzo Librandi, Nov 26 2010

G.f.: 3*x*(1+6*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011

a(n) = n + A226491(n). - Bruno Berselli, Jun 11 2013

From Elmo R. Oliveira, Dec 15 2024: (Start)

E.g.f.: 3*exp(x)*x*(2 + 7*x)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)