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%I #38 Jan 17 2023 09:24:07
%S 0,1,20,41,80,121,180,241,320,401,500,601,720,841,980,1121,1280,1441,
%T 1620,1801,2000,2201,2420,2641,2880,3121,3380,3641,3920,4201,4500,
%U 4801,5120,5441,5780,6121,6480,6841,7220,7601,8000,8401,8820,9241,9680,10121
%N Concentric 20-gonal numbers.
%C Concentric icosagonal numbers.
%C Sequence found by reading the line from 0, in the direction 0, 20, ..., and the same line from 1, in the direction 1, 41, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Main axis, perpendicular to A124080 in the same spiral.
%H Vincenzo Librandi, <a href="/A195148/b195148.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 From _Vincenzo Librandi_, Sep 27 2011: (Start)
%F a(n) = 5*n^2 + 2*(-1)^n-2;
%F a(n) = -a(n-1) + 10*n^2 - 10*n + 1. (End)
%F G.f.: x*(1+18*x+x^2)/((1+x)*(1-x)^3). - _Bruno Berselli_, Sep 27 2011
%F Sum_{n>=1} 1/a(n) = Pi^2/120 + tan(Pi/sqrt(5))*Pi/(8*sqrt(5)). - _Amiram Eldar_, Jan 17 2023
%t LinearRecurrence[{2,0,-2,1},{0,1,20,41},50] (* _Harvey P. Dale_, Apr 08 2016 *)
%o (Magma) [5*n^2+2*(-1)^n-2: n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o (PARI) a(n)=5*n^2+2*(-1)^n-2 \\ _Charles R Greathouse IV_, Sep 28 2015
%Y A195322 and A195317 interleaved.
%Y Cf. A032528, A077221, A195142, A195143, A195145, A195146, A195147, A195149.
%Y Cf. A032527, A195048, A195049. Column 20 of A195040. - _Omar E. Pol_, Sep 29 2011
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 17 2011
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