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A195148 Concentric 20-gonal numbers.

%I A195148 #38 Jan 17 2023 09:24:07
%S A195148 0,1,20,41,80,121,180,241,320,401,500,601,720,841,980,1121,1280,1441,
%T A195148 1620,1801,2000,2201,2420,2641,2880,3121,3380,3641,3920,4201,4500,
%U A195148 4801,5120,5441,5780,6121,6480,6841,7220,7601,8000,8401,8820,9241,9680,10121
%N A195148 Concentric 20-gonal numbers.
%C A195148 Concentric icosagonal numbers.
%C A195148 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 A195148 Vincenzo Librandi, <a href="/A195148/b195148.txt">Table of n, a(n) for n = 0..10000</a>
%H A195148 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A195148 From _Vincenzo Librandi_, Sep 27 2011: (Start)
%F A195148 a(n) = 5*n^2 + 2*(-1)^n-2;
%F A195148 a(n) = -a(n-1) + 10*n^2 - 10*n + 1. (End)
%F A195148 G.f.: x*(1+18*x+x^2)/((1+x)*(1-x)^3). - _Bruno Berselli_, Sep 27 2011
%F A195148 Sum_{n>=1} 1/a(n) = Pi^2/120 + tan(Pi/sqrt(5))*Pi/(8*sqrt(5)). - _Amiram Eldar_, Jan 17 2023
%t A195148 LinearRecurrence[{2,0,-2,1},{0,1,20,41},50] (* _Harvey P. Dale_, Apr 08 2016 *)
%o A195148 (Magma) [5*n^2+2*(-1)^n-2: n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o A195148 (PARI) a(n)=5*n^2+2*(-1)^n-2 \\ _Charles R Greathouse IV_, Sep 28 2015
%Y A195148 A195322 and A195317 interleaved.
%Y A195148 Cf. A032528, A077221, A195142, A195143, A195145, A195146, A195147, A195149.
%Y A195148 Cf. A032527, A195048, A195049. Column 20 of A195040. - _Omar E. Pol_, Sep 29 2011
%K A195148 nonn,easy
%O A195148 0,3
%A A195148 _Omar E. Pol_, Sep 17 2011