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A195147 Concentric 18-gonal numbers.

%I A195147 #40 Jan 17 2023 09:24:04
%S A195147 0,1,18,37,72,109,162,217,288,361,450,541,648,757,882,1009,1152,1297,
%T A195147 1458,1621,1800,1981,2178,2377,2592,2809,3042,3277,3528,3781,4050,
%U A195147 4321,4608,4897,5202,5509,5832,6157,6498,6841,7200,7561,7938,8317,8712,9109
%N A195147 Concentric 18-gonal numbers.
%C A195147 Concentric octadecagonal numbers or concentric octakaidecagonal numbers.
%C A195147 Sequence found by reading the line from 0, in the direction 0, 18, ..., and the same line from 1, in the direction 1, 37, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Main axis, perpendicular to A027468 in the same spiral.
%H A195147 Vincenzo Librandi, <a href="/A195147/b195147.txt">Table of n, a(n) for n = 0..10000</a>
%H A195147 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A195147 G.f.: -x*(1+16*x+x^2) / ( (1+x)*(x-1)^3 ). - _R. J. Mathar_, Sep 18 2011
%F A195147 From _Vincenzo Librandi_, Sep 27 2011: (Start)
%F A195147 a(n) = (18*n^2 + 7*(-1)^n - 7)/4;
%F A195147 a(n) = -a(n-1) + 9*n^2 - 9*n + 1. (End)
%F A195147 Sum_{n>=1} 1/a(n) = Pi^2/108 + tan(sqrt(7)*Pi/6)*Pi/(6*sqrt(7)). - _Amiram Eldar_, Jan 17 2023
%t A195147 LinearRecurrence[{2, 0, -2, 1}, {0, 1, 18, 37}, 50] (* _Amiram Eldar_, Jan 17 2023 *)
%o A195147 (Magma) [(18*n^2+7*(-1)^n-7)/4: n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o A195147 (PARI) a(n)=(18*n^2+7*(-1)^n-7)/4 \\ _Charles R Greathouse IV_, Sep 28 2015
%Y A195147 A195321 and A195316 interleaved.
%Y A195147 Cf. A032528, A077221, A195142, A195143, A195145, A195146, A195148, A195149.
%Y A195147 Cf. A032527, A195047, A195048. Column 18 of A195040. - _Omar E. Pol_, Sep 29 2011
%K A195147 nonn,easy
%O A195147 0,3
%A A195147 _Omar E. Pol_, Sep 17 2011