A153783 3 times 11-gonal (or hendecagonal) numbers: 3*n*(9*n-7)/2.

0, 3, 33, 90, 174, 285, 423, 588, 780, 999, 1245, 1518, 1818, 2145, 2499, 2880, 3288, 3723, 4185, 4674, 5190, 5733, 6303, 6900, 7524, 8175, 8853, 9558, 10290, 11049, 11835, 12648, 13488, 14355, 15249, 16170, 17118, 18093, 19095

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) = (27*n^2 - 21*n)/2 = A051682(n)*3.

a(n) = 27*n + a(n-1) - 24, with n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

G.f.: 3*x*(1 + 8*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011

From G. C. Greubel, Aug 28 2016: (Start)

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

E.g.f.: (3/2)*x*(2 + 9*x)*exp(x). (End)

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 6!, 27}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
Table[3*n*(9*n-7)/2, {n, 0, 25}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 3, 33}, 25] (* G. C. Greubel, Aug 28 2016 *)

Prog

(PARI) a(n)=3*n*(9*n-7)/2 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A051682, A152995.

3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153448, A153875.

Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=27: see Comments lines of A226492.

Sequence in context: A139222 A358695 A123049 * A048911 A239345 A089015

Adjacent sequences: A153780 A153781 A153782 * A153784 A153785 A153786

Keyword

easy,nonn

Author

Omar E. Pol, Jan 02 2009

Status

approved