A153875 3 times 13-gonal (or tridecagonal) numbers: a(n) = 3*n*(11*n - 9)/2.

0, 3, 39, 108, 210, 345, 513, 714, 948, 1215, 1515, 1848, 2214, 2613, 3045, 3510, 4008, 4539, 5103, 5700, 6330, 6993, 7689, 8418, 9180, 9975, 10803, 11664, 12558, 13485, 14445, 15438, 16464, 17523, 18615, 19740, 20898, 22089

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (33*n^2 - 27*n)/2 = A051865(n)*3.

a(n) = a(n-1) + 33*n - 30, with n>0, a(0)=0. - Vincenzo Librandi, Dec 14 2010

G.f.: 3*x*(1 + 10*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011

From G. C. Greubel, Aug 31 2016: (Start)

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

E.g.f.: (3/2)*x*(2 + 11*x)*exp(x). (End)

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 7!, 33}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
LinearRecurrence[{3, -3, 1}, {0, 3, 39}, 25] (* or *) Table[33*n^2 - 27*n)/2, {n, 0, 25}] (* G. C. Greubel, Aug 31 2016 *)

Prog

(PARI) a(n)=3*n*(11*n-9)/2 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A051865, A152997.

3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153783, A153448.

Cf. numbers of the form n*(n*k-k+6)/2, this sequence is the case k=33: see Comments lines of A226492.

Sequence in context: A183182 A277713 A134106 * A082954 A209366 A292542

Adjacent sequences: A153872 A153873 A153874 * A153876 A153877 A153878

Keyword

nonn,easy

Author

Omar E. Pol, Jan 03 2009

Status

approved