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%I #21 Oct 15 2023 09:27:22
%S 1,10,50,210,850,3410,13650,54610,218450,873810,3495250,13981010,
%T 55924050,223696210,894784850,3579139410,14316557650,57266230610,
%U 229064922450,916259689810,3665038759250,14660155037010,58640620148050
%N Expansion of (1+x)(1+4x)/((1-x)(1-4x)).
%H Harvey P. Dale, <a href="/A086462/b086462.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F a(0) = 1, a(1) = 10, a(2) = 50, a(n) = 5*a(n-1) - 4*a(n-2).
%F a(n) = 10*(4^n-1)/3 + 0^n = 10*A002450(n) + 0^n = 10*A001045(2*n) + 0^n.
%t CoefficientList[Series[(1+x)(1+4x)/((1-x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{5,-4},{1,10,50},30] (* _Harvey P. Dale_, May 27 2023 *)
%o (PARI) a(n) = 0^n + 10*(4^n-1)/3; \\ _Ruud H.G. van Tol_, Oct 11 2023
%Y Cf. A001045, A002450, A072197.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jul 21 2003
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