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%I #18 Sep 08 2022 08:45:54
%S 0,1,4,26,144,836,4784,27496,157824,906256,5203264,29875616,171535104,
%T 984896576,5654937344,32468715136,186424233984,1070384087296,
%U 6145778689024,35286955629056,202605609406464,1163291993916416,6679224069730304,38349816218085376
%N a(n) = 4*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.
%H Nathaniel Johnston, <a href="/A180226/b180226.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, 10).
%F a(n) = ((2+sqrt(14))^(n-1) - (2-sqrt(14))^(n-1))/(2*sqrt(14)). - _Rolf Pleisch_, May 14 2011
%F G.f.: x^2/(1-4*x-10*x^2).
%t Join[{a=0,b=1},Table[c=4*b+10*a;a=b;b=c,{n,100}]]
%t LinearRecurrence[{4,10}, {0,1}, 30] (* _G. C. Greubel_, Jan 16 2018 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(x^2/(1-4*x-10*x^2))) \\ _G. C. Greubel_, Jan 16 2018
%o (Magma) I:=[0,1]; [n le 2 select I[n] else 4*Self(n-1) + 10*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 16 2018
%Y Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015443, A015447, A030195, A053404, A057087, A083858, A085939, A090017, A091914, A099012, A180222.
%K nonn,easy
%O 1,3
%A _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011
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