|
|
A165312
|
|
a(0)=1, a(1)=5, a(n)=11*a(n-1)-25*a(n-2) for n>1.
|
|
3
|
|
|
1, 5, 30, 205, 1505, 11430, 88105, 683405, 5314830, 41378005, 322287305, 2510710230, 19560629905, 152399173205, 1187375157630, 9251147403805, 72078242501105, 561581982417030, 4375445744059705, 34090353624231005
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(n)/a(n-1) tends to (11+sqrt(21))/2 = 7.79128784...
For n>=2, a(n) equals 5^n times the permanent of the (2n-2)X(2n-2) tridiagonal matrix with 1/sqrt(5)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. [John M. Campbell, Jul 08 2011]
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1-6x)/(1-11x+25x^2).
a(n) = Sum_{k=0..n} A165253(n,k)*5^(n-k).
a(n) = ((21-sqrt(21))*(11+sqrt(21))^n+(21+sqrt(21))*(11-sqrt(21))^n )/(42*2^n). [Klaus Brockhaus, Sep 26 2009]
|
|
MATHEMATICA
|
LinearRecurrence[{11, -25}, {1, 5}, 30] (* Harvey P. Dale, Oct 02 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|