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A165323 a(0)=1, a(1)=8, a(n)=17*a(n-1)-64*a(n-2) for n>1. 2
1, 8, 72, 712, 7496, 81864, 911944, 10263752, 116119368, 1317149128, 14959895624, 170020681416, 1932918264136, 21978286879688, 249924108049992, 2842099476549832, 32320548186147656, 367554952665320904 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to (17+sqrt(33))/2 = 11.3722813...
For n>=2, a(n) equals 8^n times the permanent of the (2n-2) X (2n-2) tridiagonal matrix with 1/sqrt(8)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. [John M. Campbell, Jul 08 2011]
LINKS
FORMULA
G.f.: (1-9*x)/(1-17*x+64*x^2).
a(n) = Sum_{k=0..n} A165253(n,k)*8^(n-k).
a(n) = ((33-sqrt(33))*(17+sqrt(33))^n+(33+sqrt(33))*(17-sqrt(33))^n)/(66*2^n). [Klaus Brockhaus, Sep 28 2009]
MATHEMATICA
LinearRecurrence[{17, -64}, {1, 8}, 20] (* Harvey P. Dale, Jun 08 2018 *)
CROSSREFS
Cf. A165253.
Sequence in context: A145303 A098411 A220741 * A082366 A221159 A049388
KEYWORD
nonn
AUTHOR
Philippe Deléham, Sep 14 2009
STATUS
approved

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Last modified March 28 03:28 EDT 2024. Contains 371235 sequences. (Running on oeis4.)