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a(n) = 15*n-7.
3

%I #35 Aug 23 2021 08:11:23

%S 8,23,38,53,68,83,98,113,128,143,158,173,188,203,218,233,248,263,278,

%T 293,308,323,338,353,368,383,398,413,428,443,458,473,488,503,518,533,

%U 548,563,578,593,608,623,638,653,668,683,698,713,728,743,758,773,788

%N a(n) = 15*n-7.

%C Alternative definition: numbers m such that (13*m+1)/15 is an integer.

%C The previous comment is the case t=0 of ((13-t*(t+1))*m + t*(t+1)/2 + 1)/15, where t = 0, 1, 2 or 3. - _Bruno Berselli_, Feb 22 2016

%H Vincenzo Librandi, <a href="/A164284/b164284.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: x*(8+7*x)/(x-1)^2.

%F E.g.f.: 7 + (15*x - 7)*exp(x). - _G. C. Greubel_, Sep 12 2017

%t Range[8, 1000, 15] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)

%t LinearRecurrence[{2,-1},{8,23},60] (* _Harvey P. Dale_, Dec 25 2016 *)

%o (PARI) x='x+O('x^50); Vec(x*(8+7*x)/(x-1)^2) \\ _G. C. Greubel_, Sep 12 2017

%o (Python)

%o def a(n): return 15*n - 7

%o print([a(n) for n in range(1, 54)]) # _Michael S. Branicky_, Aug 23 2021

%Y Cf. A008597, A139606.

%Y Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Aug 12 2009

%E Definition simplified by _R. J. Mathar_, Aug 21 2009