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%I #29 Jan 17 2023 09:24:14
%S 0,1,21,43,84,127,189,253,336,421,525,631,756,883,1029,1177,1344,1513,
%T 1701,1891,2100,2311,2541,2773,3024,3277,3549,3823,4116,4411,4725,
%U 5041,5376,5713,6069,6427,6804,7183,7581,7981,8400,8821,9261,9703,10164
%N Concentric 21-gonal numbers.
%H Ivan Panchenko, <a href="/A195049/b195049.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) = 21*n^2/4 + 17*((-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+19*x+x^2)/((1-x)^3*(1+x)). (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/126 + tan(sqrt(17/21)*Pi/2)*Pi/sqrt(357). - _Amiram Eldar_, Jan 17 2023
%p A195049:=n->21*n^2/4+17*((-1)^n-1)/8: seq(A195049(n), n=0..100); # _Wesley Ivan Hurt_, Jan 17 2017
%t LinearRecurrence[{2, 0, -2, 1}, {0, 1, 21, 43}, 50] (* _Amiram Eldar_, Jan 17 2023 *)
%o (PARI) a(n)=21*n^2/4+17*((-1)^n-1)/8 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Column 21 of A195040.
%Y Cf. A032527, A032528, A195048, A195148, A195149, A195058.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 27 2011
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