A289414 a(n) = ((10-sqrt(10))^n + (10+sqrt(10))^n) / 2.

1, 10, 110, 1300, 16100, 205000, 2651000, 34570000, 452810000, 5944900000, 78145100000, 1027861000000, 13524161000000, 177975730000000, 2342340110000000, 30828986500000000, 405769120100000000, 5340773617000000000, 70296251531000000000, 925255405090000000000

Offset: 0

Author

Colin Barker, Jul 06 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..850
• Index entries for linear recurrences with constant coefficients, signature (20,-90).

Crossrefs

Cf. A083881, A090139, A143079, A145301, A145302, A145303, A289415.

Programs

Maple

a:= n-> (<<0|1>, <-90|20>>^n. <<1,10>>)[1,1]:
seq(a(n), n=0..25);  # Alois P. Heinz, Jul 06 2017

Mathematica

LinearRecurrence[{20, -90}, {1, 10}, 20] (* Jean-François Alcover, Jan 29 2025 *)

PARI

Vec((1 - 10*x) / (1 - 20*x + 90*x^2) + O(x^25))

Formula

G.f.: (1 - 10*x) / (1 - 20*x + 90*x^2).

a(n) = 20*a(n-1) - 90*a(n-2) for n>1.