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 A142588 #23 Oct 01 2024 21:11:04
%S A142588 0,5,70,985,13860,195025,2744210,38613965,543339720,7645370045,
%T A142588 107578520350,1513744654945,21300003689580,299713796309065,
%U A142588 4217293152016490,59341817924539925,835002744095575440,11749380235262596085,165326326037771920630,2326317944764069484905
%N A142588 A trisection of A000129, the Pell numbers.
%H A142588 Colin Barker, <a href="/A142588/b142588.txt">Table of n, a(n) for n = 0..850</a>
%H A142588 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,1).
%F A142588 a(n) = A000129(3n).
%F A142588 From _R. J. Mathar_, Sep 22 2008: (Start)
%F A142588 G.f.: 5*x/(1-14*x-x^2).
%F A142588 a(n) = 5*A041085(n-1). (End)
%F A142588 a(n) = ( (7+5*sqrt(2))^n - (7-5*sqrt(2))^n )/( 2*sqrt(2) ). - _Colin Barker_, Jan 25 2016
%t A142588 LinearRecurrence[{14,1},{0,5},20] (* _Harvey P. Dale_, Jul 05 2019 *)
%t A142588 Fibonacci[3*Range[0, 30], 2] (* _G. C. Greubel_, Apr 13 2021 *)
%o A142588 (PARI) concat(0, Vec(5*x/(1-14*x-x^2) + O(x^20))) \\ _Colin Barker_, Jan 25 2016
%o A142588 (Magma) [n le 2 select 5*(n-1) else 14*Self(n-1) +Self(n-2): n in [1..31]]; // _G. C. Greubel_, Apr 13 2021
%o A142588 (Sage) [lucas_number1(3*n,2,-1) for n in (0..30)] # _G. C. Greubel_, Apr 13 2021
%Y A142588 Cf. A000129, A041085.
%K A142588 nonn,easy
%O A142588 0,2
%A A142588 _Paul Curtz_, Sep 22 2008
%E A142588 Changed offset and extended by _R. J. Mathar_, Sep 22 2008