This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082639 #50 Nov 10 2024 13:01:51
%S A082639 0,2,16,98,576,3362,19600,114242,665856,3880898,22619536,131836322,
%T A082639 768398400,4478554082,26102926096,152139002498,886731088896,
%U A082639 5168247530882,30122754096400,175568277047522,1023286908188736
%N A082639 Numbers k such that 2*k*(k+2) is a square.
%C A082639 Even-indexed terms are squares. Their square roots form sequence A005319. Odd-indexed terms divided by 2 are squares. Their square roots form the sequence A002315. (Index starts at 0.)
%C A082639 Lower of two terms with difference 2 in A088827. - _Ophir Spector_, Nov 06 2024
%H A082639 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F A082639 a(n) = A001541(n) - 1.
%F A082639 a(n) = (1/2)*(s^n + t^n) - 1, where s = 3 + 2*sqrt(2), t = 3 - 2*sqrt(2). Note: s=1/t. a(n) = 6*a(n-1) - a(n-2) + 4, a(0)=0, a(1)=2.
%F A082639 a(n) = 1/kappa(sqrt(2)/A001542(n)); a(n) = 1/kappa(sqrt(8)/A005319(n)) where kappa(x) is the sum of successive remainders by computing the Euclidean algorithm for (1, x). - _Thomas Baruchel_, Nov 29 2003
%F A082639 G.f.: -2*x^2*(x+1)/((x-1)*(x^2-6*x+1)). - _Colin Barker_, Nov 22 2012
%t A082639 a[0] = 0; a[1] = 2; a[n_] := a[n] = 6a[n - 1] - a[n - 2] + 4; Table[ a[n], {n, 0, 20}]
%t A082639 LinearRecurrence[{7,-7,1},{0,2,16},30] (* _Harvey P. Dale_, Nov 21 2015 *)
%Y A082639 Cf. A001541, A002315, A005319, A088827.
%K A082639 easy,nonn
%O A082639 1,2
%A A082639 _James R. Buddenhagen_, May 15 2003
%E A082639 More terms from _Robert G. Wilson v_, May 15 2003