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A163114 a(n) = 5*a(n-2) for n > 2; a(1) = 3, a(2) = 5.

%I A163114 #24 Feb 03 2025 10:06:38
%S A163114 3,5,15,25,75,125,375,625,1875,3125,9375,15625,46875,78125,234375,
%T A163114 390625,1171875,1953125,5859375,9765625,29296875,48828125,146484375,
%U A163114 244140625,732421875,1220703125,3662109375,6103515625,18310546875
%N A163114 a(n) = 5*a(n-2) for n > 2; a(1) = 3, a(2) = 5.
%C A163114 Binomial transform is A163062, second binomial transform is A163063, third binomial transform is A098648 without initial 1, fourth binomial transform is A163064, fifth binomial transform is A163065.
%H A163114 G. C. Greubel, <a href="/A163114/b163114.txt">Table of n, a(n) for n = 1..1000</a>
%H A163114 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,5).
%F A163114 a(n) = (2-(-1)^n)*5^(1/4*(2*n-1+(-1)^n)).
%F A163114 G.f.: x*(3+5*x)/(1-5*x^2).
%F A163114 a(n) = A056487(n), n>=1.
%F A163114 E.g.f.: cosh(sqrt(5)*x) + 3*sinh(sqrt(5)*x)/sqrt(5) - 1. - _Stefano Spezia_, Nov 19 2023
%t A163114 CoefficientList[Series[x*(3 + 5*x)/(1 - 5*x^2), {x, 0, 50}], x] (* _G. C. Greubel_, Dec 21 2017 *)
%t A163114 LinearRecurrence[{0,5},{3,5},30] (* _Harvey P. Dale_, Aug 01 2021 *)
%o A163114 (Magma) [ n le 2 select 2*n+1 else 5*Self(n-2): n in [1..29] ];
%o A163114 (PARI) x='x+O('x^30); Vec(x*(3+5*x)/(1-5*x^2)) \\ _G. C. Greubel_, Dec 21 2017
%Y A163114 Cf. A056487, A098648, A163062, A163063, A163064, A163065, A111386.
%K A163114 nonn,easy
%O A163114 1,1
%A A163114 _Klaus Brockhaus_, Jul 21 2009