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%I #30 May 07 2024 07:11:16
%S 1,41,121,241,401,601,841,1121,1441,1801,2201,2641,3121,3641,4201,
%T 4801,5441,6121,6841,7601,8401,9241,10121,11041,12001,13001,14041,
%U 15121,16241,17401,18601,19841,21121,22441,23801,25201,26641,28121,29641,31201,32801
%N Centered 40-gonal numbers.
%C Also centered tetracontagonal numbers or centered tetrakaicontagonal numbers. Also sequence found by reading the line from 1, in the direction 1, 41, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Semi-axis opposite to A195322 in the same spiral.
%H Vincenzo Librandi, <a href="/A195317/b195317.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 20*n^2 - 20*n + 1.
%F Sum_{n>=1} 1/a(n) = Pi*tan(Pi/sqrt(5))/(8*sqrt(5)). - _Amiram Eldar_, Feb 11 2022
%F G.f.: -x*(1+38*x+x^2)/(x-1)^3 . - _R. J. Mathar_, May 07 2024
%t Table[20*n^2 - 20*n + 1, {n, 1, 40}] (* _Amiram Eldar_, Feb 11 2022 *)
%o (Magma) [20*n^2 - 20*n + 1: n in [1..50]]; // _Vincenzo Librandi_, Sep 21 2011
%o (PARI) a(n)=20*n^2-20*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Bisection of A195148.
%Y Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195316, A195318.
%K nonn,easy
%O 1,2
%A _Omar E. Pol_, Sep 16 2011
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