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%I #18 Sep 08 2022 08:45:28
%S 1,7,63,469,4025,31031,259287,2039093,16783249,133482055,1089343311,
%T 8719307317,70816436873,568878932279,4607763271335,37090594224341,
%U 299961588744097,2417362294480903,19532842437422559,157516437304409365
%N Expansion of x*(1 + 5*x)/(1 - 2*x - 49*x^2).
%H G. C. Greubel, <a href="/A123009/b123009.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,49).
%F From _Colin Barker_, Oct 19 2012: (Start)
%F a(n) = 2*a(n-1) + 49*a(n-2) for n>2.
%F G.f.: x*(1 +5*x)/(1 -2*x -49*x^2). (End)
%F a(n) = (7*i)^(n-2)*(5*ChebyshevU(n-2, -i/7) + 7*i*ChebyshevU(n-1, -i/7)). - _G. C. Greubel_, Jul 13 2021
%t M:= {{0, 7}, {7, 2}}; v[1]= {1, 1}; v[n_]:= v[n]= M.v[n-1];
%t Table[v[n][[1]], {n, 30}]
%o (Magma) [n le 2 select 7^(n-1) else 2*Self(n-1) + 25*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Jul 13 2021
%o (Sage) [(7*i)^(n-2)*(5*chebyshev_U(n-2, -i/7) + 7*i*chebyshev_U(n-1, -i/7)) for n in (1..30)] # _G. C. Greubel_, Jul 13 2021
%Y Cf. A002534, A123005.
%K nonn,easy
%O 1,2
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 23 2006
%E Sequence edited by _Joerg Arndt_ and _Colin Barker_, Oct 19 2012
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