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
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
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
Programs
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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 *) -
PARI
a(n)=n*(7*n-5) \\ Charles R Greathouse IV, Jun 17 2017
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
From Elmo R. Oliveira, Dec 27 2024: (Start)
E.g.f.: exp(x)*x*(2 + 7*x).
a(n) = n + A051868(n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)