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%I #27 Jan 17 2023 09:56:17
%S 0,1,19,39,76,115,171,229,304,381,475,571,684,799,931,1065,1216,1369,
%T 1539,1711,1900,2091,2299,2509,2736,2965,3211,3459,3724,3991,4275,
%U 4561,4864,5169,5491,5815,6156,6499,6859,7221,7600,7981,8379,8779,9196
%N Concentric 19-gonal numbers.
%C Also concentric enneadecagonal numbers.
%H Ivan Panchenko, <a href="/A195048/b195048.txt">Table of n, a(n) for n = 0..1000</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) = (19/4)*n^2 + (15/8)*((-1)^n - 1).
%F From _Colin Barker_, Sep 16 2012: (Start)
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F G.f.: x*(1 + 17*x + x^2)/((1-x)^3*(1+x)). (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/114 + tan(sqrt(15/19)*Pi/2)*Pi/sqrt(285). - _Amiram Eldar_, Jan 17 2023
%t LinearRecurrence[{2,0,-2,1},{0,1,19,39},50] (* _Harvey P. Dale_, May 17 2016 *)
%o (PARI) a(n)=19*n^2/4+15*((-1)^n-1)/8 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Column 19 of A195040.
%Y Cf. A032527, A032528, A195047, A195147, A195148, A195049.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 27 2011