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%I #36 Jan 16 2023 08:53:35
%S 0,1,16,33,64,97,144,193,256,321,400,481,576,673,784,897,1024,1153,
%T 1296,1441,1600,1761,1936,2113,2304,2497,2704,2913,3136,3361,3600,
%U 3841,4096,4353,4624,4897,5184,5473,5776,6081,6400,6721,7056,7393,7744,8097,8464
%N Concentric 16-gonal numbers.
%C Concentric hexadecagonal numbers or concentric hexakaidecagonal numbers.
%C Sequence found by reading the line from 0, in the direction 0, 16, ..., and the same line from 1, in the direction 1, 33, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. Main axis, perpendicular to A033996 in the same spiral.
%H Vincenzo Librandi, <a href="/A195146/b195146.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) = (8*n^2 + 3*(-1)^n - 3)/2;
%F a(n) = -a(n-1) + 8*n^2 - 8*n + 1. (End)
%F G.f. -x*(1+14*x+x^2) / ( (1+x)*(x-1)^3 ). - _R. J. Mathar_, Sep 18 2011
%F Sum_{n>=1} 1/a(n) = Pi^2/96 + tan(sqrt(3)*Pi/4)*Pi/(8*sqrt(3)). - _Amiram Eldar_, Jan 16 2023
%t LinearRecurrence[{2, 0, -2, 1}, {0, 1, 16, 33}, 50] (* _Amiram Eldar_, Jan 16 2023 *)
%o (Magma) [(8*n^2+3*(-1)^n-3)/2: n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o (PARI) a(n)=(8*n^2+3*(-1)^n-3)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A016802 and A195315 interleaved.
%Y Cf. A032528, A033996, A074377, A077221, A195142, A195143, A195145, A195147, A195148, A195149.
%Y Column 16 of A195040.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 17 2011
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