A139268 Twice nonagonal numbers (or twice 9-gonal numbers): a(n) = n*(7*n-5).

0, 2, 18, 48, 92, 150, 222, 308, 408, 522, 650, 792, 948, 1118, 1302, 1500, 1712, 1938, 2178, 2432, 2700, 2982, 3278, 3588, 3912, 4250, 4602, 4968, 5348, 5742, 6150, 6572, 7008, 7458, 7922, 8400, 8892, 9398, 9918, 10452, 11000

Offset

0,2

Links

Table of n, a(n) for n=0..40.

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

Formula

a(n) = 2*A001106(n) = 7*n^2 - 5*n = n*(7*n-5).

a(n) = 14*n + a(n-1) - 12, with a(0)=0. - Vincenzo Librandi, Aug 03 2010

G.f.: 2*x*(1 + 6*x)/(1 - x)^3. - Philippe Deléham, Apr 03 2013

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 2, 6!, 14}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
2*PolygonalNumber[9, Range[0, 40]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 2, 18}, 50] (* Harvey P. Dale, Feb 08 2024 *)

Prog

(PARI) a(n)=n*(7*n-5) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A001106.

Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=14). - Bruno Berselli, Jun 10 2013

Sequence in context: A009820 A304933 A126909 * A052681 A208652 A223469

Adjacent sequences: A139265 A139266 A139267 * A139269 A139270 A139271

Keyword

nonn,easy

Author

Omar E. Pol, May 15 2008

Status

approved