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A017461 a(n) = 11*n + 6.

%I A017461 #34 Apr 12 2025 09:50:00
%S A017461 6,17,28,39,50,61,72,83,94,105,116,127,138,149,160,171,182,193,204,
%T A017461 215,226,237,248,259,270,281,292,303,314,325,336,347,358,369,380,391,
%U A017461 402,413,424,435,446,457,468,479,490,501,512,523,534,545,556,567,578,589
%N A017461 a(n) = 11*n + 6.
%H A017461 Vincenzo Librandi, <a href="/A017461/b017461.txt">Table of n, a(n) for n = 0..10000</a>
%H A017461 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A017461 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017461 a(0)=6, a(1)=17; for n>1, a(n) = 2*a(n-1) - a(n-2). - _Harvey P. Dale_, Apr 14 2015
%F A017461 From _G. C. Greubel_, Sep 19 2019: (Start)
%F A017461 G.f.: (6 + 5*x)/(1-x)^2.
%F A017461 E.g.f.: (6 + 11*x)*exp(x). (End)
%F A017461 a(n) = A141694(n)/2. - _Elmo R. Oliveira_, Apr 11 2025
%p A017461 seq(11*n+6, n=0..60); # _G. C. Greubel_, Sep 19 2019
%t A017461 Range[6, 1000, 11] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t A017461 LinearRecurrence[{2,-1},{6,17},60] (* or *) NestList[11 + #&, 6, 60] (* _Harvey P. Dale_, Apr 14 2015 *)
%o A017461 (Magma) [11*n+6: n in [0..60]]; // _Vincenzo Librandi_, Sep 03 2011
%o A017461 (PARI) a(n)=11*n+6 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A017461 (Sage) [11*n+6 for n in (0..60)] # _G. C. Greubel_, Sep 19 2019
%o A017461 (GAP) List([0..60], n-> 11*n+6); # _G. C. Greubel_, Sep 19 2019
%Y A017461 Cf. A008593, A017401, A017449, A141694.
%Y A017461 Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.
%Y A017461 Powers of the form (11*n+6)^m: this sequence (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).
%K A017461 nonn,easy
%O A017461 0,1
%A A017461 _N. J. A. Sloane_