|
%I #7 Mar 18 2023 18:07:20
%S 1,5,5,25,25,125,125,625,625,3125,3125,15625,15625,78125,78125,390625,
%T 390625,1953125,1953125,9765625,9765625,48828125,48828125,244140625,
%U 244140625,1220703125,1220703125,6103515625,6103515625,30517578125
%N a(n) = 5*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
%C Apparently a(n) = A074872(n+1), a(n) = A056451(n-1) for n > 1.
%C 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,5).
%F a(n) = 5^((1/4)*(2*n-1+(-1)^n)).
%F G.f.: x*(1+5*x)/(1-5*x^2).
%t LinearRecurrence[{0,5},{1,5},30] (* _Harvey P. Dale_, Mar 18 2023 *)
%o (Magma) [ n le 2 select 4*n-3 else 5*Self(n-2): n in [1..30] ];
%Y Cf. A000351 (powers of 5), A074872 (powers of 5 repeated), A056451 (5^floor((n+1)/2)), A084057, A048876, A082762, A162769, A093145.
%K nonn,easy
%O 1,2
%A _Klaus Brockhaus_, Jul 19 2009
|
