A164551 a(n) = 10*a(n-1)-19*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

1, 9, 71, 539, 4041, 30169, 224911, 1675899, 12485681, 93014729, 692919351, 5161913659, 38453668921, 286460329689, 2133983587391, 15897089609819, 118425207937761, 882207376791049, 6571994817093031, 48958008011900379

Offset: 0

Author

Klaus Brockhaus, Aug 15 2009

Keywords

• nonn

Comments

Binomial transform of A154235. Inverse binomial transform of A164552.

Links

• Index entries for linear recurrences with constant coefficients, signature (10, -19).

Crossrefs

Cf. A154235, A164552.

Programs

Magma

[ n le 2 select 8*n-7 else 10*Self(n-1)-19*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{10,-19},{1,9},30] (* Harvey P. Dale, Dec 26 2015 *)

Formula

a(n) = ((3+2*sqrt(6))*(5+sqrt(6))^n+(3-2*sqrt(6))*(5-sqrt(6))^n)/6.

G.f.: (1-x)/(1-10*x+19*x^2).