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%I #33 Jan 17 2023 09:23:53
%S 0,1,24,49,96,145,216,289,384,481,600,721,864,1009,1176,1345,1536,
%T 1729,1944,2161,2400,2641,2904,3169,3456,3745,4056,4369,4704,5041,
%U 5400,5761,6144,6529,6936,7345,7776,8209,8664,9121,9600,10081,10584,11089
%N Concentric 24-gonal numbers.
%C Sequence found by reading the line from 0, in the direction 0, 24, ..., and the same line from 1, in the direction 1, 49, ..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818. Main axis, perpendicular to A049598 in the same spiral.
%H Vincenzo Librandi, <a href="/A195158/b195158.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) = 6*n^2 + 5*((-1)^n-1)/2.
%F a(n) = -a(n-1) + A069190(n). - _Vincenzo Librandi_, Sep 30 2011
%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+22*x+x^2)/((1-x)^3*(1+x)). (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/144 + tan(sqrt(5/6)*Pi/2)*Pi/(4*sqrt(30)). - _Amiram Eldar_, Jan 17 2023
%t LinearRecurrence[{2,0,-2,1},{0,1,24,49},50] (* _Harvey P. Dale_, Jan 28 2021 *)
%o (Magma) [(12*n^2+5*(-1)^n-5)/2: n in [0..50]]; // _Vincenzo Librandi_, Sep 30 2011
%o (PARI) a(n)=6*n^2+5*((-1)^n-1)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Column 24 of A195040.
%Y Cf. A032527, A032528, A195143, A195149, A195058.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 28 2011
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