A163462 a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

1, 11, 122, 1362, 15284, 172204, 1946248, 22048968, 250247056, 2844142256, 32358633632, 368446731552, 4197788535104, 47847991009984, 545576543759488, 6222427756211328, 70982053835796736, 809843156607224576

Offset: 0

Author

Klaus Brockhaus, Jul 28 2009

Keywords

• nonn

Comments

Binomial transform of A163461. Tenth binomial transform of A016116.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (20, -98).

Crossrefs

Cf. A163461, A016116 (powers of 2 doubled up).

Programs

Magma

[ n le 2 select 10*n-9 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{20,-98},{1,11},30] (* Harvey P. Dale, Dec 04 2011 *)
CoefficientList[Series[(1 - 9 x)/(1 - 20 x + 98 x^2), {x, 0, 17}], x] (* Michael De Vlieger, Dec 25 2016 *)

PARI

Vec((1-9*x)/(1-20*x+98*x^2) + O(x^50)) \\ G. C. Greubel, Dec 25 2016

Formula

a(n) = ((2+sqrt(2))*(10+sqrt(2))^n + (2-sqrt(2))*(10-sqrt(2))^n)/4.

G.f.: (1-9*x)/(1-20*x+98*x^2).

E.g.f.: (1/2)*exp(10*x)*( 2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 25 2016