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

1, 5, 5, 25, 25, 125, 125, 625, 625, 3125, 3125, 15625, 15625, 78125, 78125, 390625, 390625, 1953125, 1953125, 9765625, 9765625, 48828125, 48828125, 244140625, 244140625, 1220703125, 1220703125, 6103515625, 6103515625, 30517578125

Offset: 1

Author

Klaus Brockhaus, Jul 19 2009

Keywords

• nonn
• easy

Comments

Apparently a(n) = A074872(n+1), a(n) = A056451(n-1) for n > 1.

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.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,5).

Crossrefs

Cf. A000351 (powers of 5), A074872 (powers of 5 repeated), A056451 (5^floor((n+1)/2)), A084057, A048876, A082762, A162769, A093145.

Programs

Magma

[ n le 2 select 4*n-3 else 5*Self(n-2): n in [1..30] ];

Mathematica

LinearRecurrence[{0,5},{1,5},30] (* Harvey P. Dale, Mar 18 2023 *)

Formula

a(n) = 5^((1/4)*(2*n-1+(-1)^n)).

G.f.: x*(1+5*x)/(1-5*x^2).