OFFSET
0,2
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).
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
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 *)
PROG
(Magma) [ n le 2 select 11*n-10 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];
(PARI) Vec((1-8*x)/(1-20*x+98*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Jul 27 2009
STATUS
approved