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%I #9 Aug 05 2018 13:34:17
%S 0,1,3,31,78,781,1953,19531,48828,488281,1220703,12207031,30517578,
%T 305175781,762939453,7629394531,19073486328,190734863281,476837158203,
%U 4768371582031,11920928955078,119209289550781,298023223876953,2980232238769531,7450580596923828
%N a(n) = (5^n - 1)/(2^(3 - (n mod 2))).
%H Colin Barker, <a href="/A152417/b152417.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,26,0,-25).
%F a(n) = (5^n - 1)/(2^(3 - (n mod 2))).
%F From _Colin Barker_, Nov 16 2015: (Start)
%F a(n) = (5^n-1)/8 for n even.
%F a(n) = (5^n-1)/4 for n odd.
%F a(n) = 26*a(n-2)-25*a(n-4) for n>3.
%F G.f.: x*(5*x^2+3*x+1) / ((x-1)*(x+1)*(5*x-1)*(5*x+1)).
%F (End)
%t a[n_] := (5^n - 1)/(2^(3 - Mod[n, 2]));
%t Table[a[n], {n, 0, 30}]
%t LinearRecurrence[{0,26,0,-25},{0,1,3,31},30] (* _Harvey P. Dale_, Aug 05 2018 *)
%o (PARI) concat(0, Vec(x*(5*x^2+3*x+1) / ((x-1)*(x+1)*(5*x-1)*(5*x+1)) + O(x^30))) \\ _Colin Barker_, Nov 16 2015
%Y Cf. A003462.
%K nonn,easy
%O 0,3
%A _Roger L. Bagula_, Dec 03 2008
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