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%I #49 Jan 02 2024 08:54:50
%S 1,2,7,17,52,137,397,1082,3067,8477,23812,66197,185257,516242,1442527,
%T 4023737,11236372,31355057,87536917,244312202,681996787,1903557797,
%U 5313541732,14831330717,41399039377,115555692962,322550889847
%N a(n) = a(n-1) + 5*a(n-2) for n >= 2, a(0)=1, a(1)=2.
%H Alois P. Heinz, <a href="/A133407/b133407.txt">Table of n, a(n) for n = 0..1000</a> (first 100 terms from Matt C. Anderson)
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,5).
%F G.f.: (1+x)/(1-x-5*x^2).
%F a(n) = Sum_{k=0..n+1} A122950(n+1,k)*4^(n+1-k). - _Philippe Deléham_, Jan 08 2008
%F a(n) = ((21 - 3*sqrt(21))/42)*(1/2 - (1/2)*sqrt(21))^n + ((21 + 3*sqrt(21))/42)*(1/2 + (1/2)*sqrt(21))^n. - _Richard Choulet_, Nov 20 2008
%t LinearRecurrence[{1,5},{1,2},30] (* _Harvey P. Dale_, Jul 23 2013 *)
%o (PARI) x='x+O('x^99); Vec((1+x)/(1-x-5*x^2)) \\ _Altug Alkan_, Aug 28 2017
%Y Cf. A030195 (shifted binomial transform).
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Jan 03 2008