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%I #28 Jul 22 2023 18:43:11
%S 0,1,23,47,92,139,207,277,368,461,575,691,828,967,1127,1289,1472,1657,
%T 1863,2071,2300,2531,2783,3037,3312,3589,3887,4187,4508,4831,5175,
%U 5521,5888,6257,6647,7039,7452,7867,8303,8741,9200,9661,10143,10627
%N Concentric 23-gonal numbers.
%H Ivan Panchenko, <a href="/A195058/b195058.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) = 23*n^2/4 + 19*((-1)^n-1)/8.
%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 + 21*x + x^2)/((1-x)^3*(1+x)). (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/138 + tan(sqrt(19/23)*Pi/2)*Pi/sqrt(437). - _Amiram Eldar_, Jan 17 2023
%t Table[23n^2/4 + 19((-1)^n - 1)/8, {n, 0, 49}] (* _Alonso del Arte_, Jan 23 2015 *)
%t LinearRecurrence[{2,0,-2,1},{0,1,23,47},50] (* _Harvey P. Dale_, Jul 22 2023 *)
%o (PARI) a(n)=23*n^2/4+19*((-1)^n-1)/8 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Column 23 of A195040.
%Y Cf. A032527, A032528, A195049, A195149, A195158.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 28 2011
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