A152759 3 times 9-gonal (or nonagonal) numbers: 3n(7n-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

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

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

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

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 *)

Prog

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

Crossrefs

Cf. A001106, A139268.

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.

Sequence in context: A204046 A305094 A120117 * A302275 A302725 A166102

Adjacent sequences: A152756 A152757 A152758 * A152760 A152761 A152762

Keyword

nonn,easy

Author

Omar E. Pol, Dec 14 2008

Status

approved