%I #43 Feb 20 2023 03:13:59

%S 1,11,26,46,71,101,136,176,221,271,326,386,451,521,596,676,761,851,

%T 946,1046,1151,1261,1376,1496,1621,1751,1886,2026,2171,2321,2476,2636,

%U 2801,2971,3146,3326,3511,3701,3896,4096,4301,4511,4726,4946,5171,5401,5636

%N a(n) = 5*n*(n+1)/2 - 4.

%C Numbers of the form 5*(h+1)*(2*h-1) + 1, where h = 0, -1, 1, -2, 2, -3, 3, -4, 4, ... . - _Bruno Berselli_, Feb 03 2017

%H Vincenzo Librandi, <a href="/A166137/b166137.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = a(n-1) + 5*n = 3*a(n-1) - 3*a(n-2) + a(n-3) = A166151(n)-1.

%F O.g.f.: x*(-1 - 8*x + 4*x^2)/(x - 1)^3. [corrected by _Georg Fischer_, May 11 2019]

%F E.g.f.: (1/2)*(-8 + 10*x + 5*x^2)*exp(x). - _G. C. Greubel_, Apr 26 2016

%F Sum_{n>=1} 1/a(n) = 1/4 + (2*Pi/sqrt(185))*tan(sqrt(37/5)*Pi/2). - _Amiram Eldar_, Feb 20 2023

%p A166137:=n->5*n*(n+1)/2-4; seq(A166137(n), n=1..100); # _Wesley Ivan Hurt_, Nov 12 2013

%t LinearRecurrence[{3, -3, 1}, {1, 11, 26}, 50] (* _Vincenzo Librandi_, Mar 15 2012 *)

%t Table[5 n (n + 1)/2 - 4, {n, 47}] (* or *)

%t Rest@ CoefficientList[Series[x (-1 - 8 x + 4 x^2)/(x - 1)^3, {x, 0, 47}], x] (* _Michael De Vlieger_, Apr 27 2016 *)

%o (PARI) for(n=1, 40, print1(5*n*(n+1)/2-4", ")); \\ _Vincenzo Librandi_, Mar 15 2012

%o (Magma) I:=[1,11,26]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Mar 15 2012

%o (Magma) [5*n*(n+1)/2-4: n in [0..40]]; // _Bruno Berselli_, Feb 03 2017

%Y Cf. A166151.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Oct 08 2009

%E Definition replaced by polynomial from _R. J. Mathar_, Oct 12 2009