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%I #25 Apr 25 2023 05:57:59
%S 16,144,400,784,1296,1936,2704,3600,4624,5776,7056,8464,10000,11664,
%T 13456,15376,17424,19600,21904,24336,26896,29584,32400,35344,38416,
%U 41616,44944,48400,51984,55696,59536,63504,67600,71824,76176,80656,85264,90000,94864,99856
%N a(n) = (8*n + 4)^2.
%H Vincenzo Librandi, <a href="/A017114/b017114.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Paul Curtz_, Nov 07 2008: (Start)
%F a(n) = 16*A016754(n).
%F a(n+2) = A061042(2n+1), from Brackett spectrum of hydrogen. (End)
%F G.f.: -16*(1 + 6*x + x^2)/(x-1)^3. - _R. J. Mathar_, Jul 14 2016
%F From _Amiram Eldar_, Apr 25 2023: (Start)
%F a(n) = A017113(n)^2.
%F a(n) = 2^2*A016826(n).
%F Sum_{n>=0} 1/a(n) = Pi^2/128.
%F Sum_{n>=0} (-1)^n/a(n) = G/16, where G is Catalan's constant (A006752). (End)
%t LinearRecurrence[{3, -3, 1},{16, 144, 400},30] (* _Ray Chandler_, Aug 04 2015 *)
%o (Magma) [(8*n+4)^2: n in [0..35] ]; // _Vincenzo Librandi_, Jul 21 2011
%o (PARI) a(n)=(8*n+4)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A006752, A016754, A016826, A017113, A061042.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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