A163166 a(n) = 20*a(n-1)-95*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 105, 1150, 13025, 151250, 1787625, 21383750, 257850625, 3125556250, 38015315625, 463378468750, 5656114390625, 69101333281250, 844695798515625, 10329289308593750, 126339685312890625, 1545511221941406250

Offset: 0

Author

Klaus Brockhaus, Jul 22 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A152261. Tenth binomial transform of powers of 5 interleaved with zeros.

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-95).

Crossrefs

Cf. A000351 (powers of 5), A152261.

Programs

Magma

[ n le 2 select 9*n-8 else 20*Self(n-1)-95*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{20,-95},{1,10},20] (* Harvey P. Dale, Jul 08 2017 *)

Formula

a(n) = ((10+sqrt(5))^n+(10-sqrt(5))^n)/2.

G.f.: (1-10*x)/(1-20*x+95*x^2).