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%I #36 Jan 16 2023 08:19:26
%S 0,1,11,23,44,67,99,133,176,221,275,331,396,463,539,617,704,793,891,
%T 991,1100,1211,1331,1453,1584,1717,1859,2003,2156,2311,2475,2641,2816,
%U 2993,3179,3367,3564,3763,3971,4181,4400,4621,4851,5083,5324,5567
%N Concentric 11-gonal numbers.
%C Also concentric hendecagonal numbers. A033584 and A069173 interleaved.
%C Partial sums of A175885. - _Reinhard Zumkeller_, Jan 07 2012
%H Vincenzo Librandi, <a href="/A195043/b195043.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n) = 11*n^2/4 + 7*((-1)^n - 1)/8.
%F a(n) = -a(n-1) + A069125(n). - _Vincenzo Librandi_, Sep 30 2011
%F From _Colin Barker_, Sep 15 2013: (Start)
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F G.f.: -x*(x^2+9*x+1) / ((x-1)^3*(x+1)). (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/66 + tan(sqrt(7/11)*Pi/2)*Pi/sqrt(77). - _Amiram Eldar_, Jan 16 2023
%t LinearRecurrence[{2,0,-2,1},{0,1,11,23},50] (* _Harvey P. Dale_, May 20 2019 *)
%o (Magma) [11*n^2/4+7*((-1)^n-1)/8: n in [0..50]]; // _Vincenzo Librandi_, Sep 30 2011
%o (Haskell)
%o a195043 n = a195043_list !! n
%o a195043_list = scanl (+) 0 a175885_list
%o -- _Reinhard Zumkeller_, Jan 07 2012
%o (PARI) Vec(-x*(x^2+9*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ _Colin Barker_, Sep 15 2013
%Y Column 11 of A195040.
%Y Cf. A032527, A032528, A033584, A069173, A175885, A195042, A195142, A195143, A195045.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 27 2011
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