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A162962 a(n) = 5*a(n-2) for n > 2; a(1) = 1, a(2) = 5.

%I A162962 #7 Mar 18 2023 18:07:20
%S A162962 1,5,5,25,25,125,125,625,625,3125,3125,15625,15625,78125,78125,390625,
%T A162962 390625,1953125,1953125,9765625,9765625,48828125,48828125,244140625,
%U A162962 244140625,1220703125,1220703125,6103515625,6103515625,30517578125
%N A162962 a(n) = 5*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
%C A162962 Apparently a(n) = A074872(n+1), a(n) = A056451(n-1) for n > 1.
%C A162962 Binomial transform is A084057 without initial 1, second binomial transform is A048876, third binomial transform is A082762, fourth binomial transform is A162769, fifth binomial transform is A093145 without initial 0.
%H A162962 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,5).
%F A162962 a(n) = 5^((1/4)*(2*n-1+(-1)^n)).
%F A162962 G.f.: x*(1+5*x)/(1-5*x^2).
%t A162962 LinearRecurrence[{0,5},{1,5},30] (* _Harvey P. Dale_, Mar 18 2023 *)
%o A162962 (Magma) [ n le 2 select 4*n-3 else 5*Self(n-2): n in [1..30] ];
%Y A162962 Cf. A000351 (powers of 5), A074872 (powers of 5 repeated), A056451 (5^floor((n+1)/2)), A084057, A048876, A082762, A162769, A093145.
%K A162962 nonn,easy
%O A162962 1,2
%A A162962 _Klaus Brockhaus_, Jul 19 2009