A163206 a(n) = 20*a(n-1) - 92*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 108, 1240, 14864, 183200, 2296512, 29075840, 370237696, 4729776640, 60533664768, 775533844480, 9941579730944, 127482480926720, 1635024283287552, 20972097420492800, 269019714347401216, 3450961324262686720, 44269412765292822528, 567899813473689272320

Offset: 0

Author

Klaus Brockhaus, Jul 28 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A152267. Tenth binomial transform of powers of 8 interleaved with zeros.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (20,-92).

Crossrefs

Cf. A152267, A001018 (powers of 8).

Programs

Magma

[ n le 2 select 9*n-8 else 20*Self(n-1)-92*Self(n-2): n in [1..17] ];

Mathematica

LinearRecurrence[{20, -92}, {1, 10}, 50] (* or *) Table[((10+Sqrt[8])^n + (10-Sqrt[8])^n)/2,{n,0,25}] (* G. C. Greubel, Dec 10 2016 *)

PARI

Vec((1-10*x)/(1-20*x+92*x^2) + O(x^50)) \\ G. C. Greubel, Dec 10 2016

Formula

a(n) = ((10+sqrt(8))^n + (10-sqrt(8))^n)/2.

G.f.: (1-10*x)/(1-20*x+92*x^2).

Extensions

Terms a(18) - a(20) added by G. C. Greubel, Dec 10 2016