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

0,2

Comments

Binomial transform of A154235. Inverse binomial transform of A164552.

Links

Table of n, a(n) for n=0..19.

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

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A154235, A164552.

Sequence in context: A226711 A231420 A081900 * A178869 A057080 A287819

Adjacent sequences: A164548 A164549 A164550 * A164552 A164553 A164554

Keyword

nonn

Author

Klaus Brockhaus, Aug 15 2009

Status

approved