A163448 a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 12.

1, 12, 142, 1664, 19364, 224208, 2586488, 29757376, 341671696, 3917211072, 44860395232, 513321219584, 5870105658944, 67096633659648, 766662318616448, 8757776273683456, 100022618249257216, 1142190290164165632

Offset: 0

Author

Klaus Brockhaus, Jul 27 2009

Keywords

• nonn

Comments

Binomial transform of A163447. Tenth binomial transform of A163403.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..940 (first 100 terms from Vincenzo Librandi)
• Index entries for linear recurrences with constant coefficients, signature (20, -98).

Crossrefs

Cf. A163403, A163447.

Programs

Magma

[ n le 2 select 11*n-10 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];

Mathematica

LinearRecurrence[{20,-98},{1,12},30] (* or *) With[{ms=10-Sqrt[2], ps=10+ Sqrt[2]},Table[Simplify[(31ms^n-41Sqrt[2](ms^n)+49ps^n+49Sqrt[2] ps^n)/ (98ps)],{n,20}]] (* Harvey P. Dale, Nov 14 2011 *)

PARI

Vec((1-8*x)/(1-20*x+98*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016

Formula

a(n) = ((1+sqrt(2))*(10+sqrt(2))^n + (1-sqrt(2))*(10-sqrt(2))^n)/2.

G.f.: (1-8*x)/(1-20*x+98*x^2).

a(n) = (31*(10-sqrt(2))^n - 41*sqrt(2)*(10-sqrt(2))^n + 49*(10+sqrt(2))^n + 49*sqrt(2)*(10+sqrt(2))^n)/(98*(10+sqrt(2))). - Harvey P. Dale, Nov 14 2011

E.g.f.: exp(10*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 24 2016