login
A165322
a(0)=1, a(1)=7, a(n)=15*a(n-1)-49*a(n-2) for n>1.
2
1, 7, 56, 497, 4711, 46312, 463841, 4688327, 47596696, 484222417, 4931098151, 50239573832, 511969798081, 5217807853447, 53180597695736, 542036380617137, 5524696422165991, 56310663682250152, 573949830547618721
OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to (15+sqrt(29))/2=10,192582...
For n>=2, a(n) equals 7^n times the permanent of the (2n-2)X(2n-2) tridiagonal matrix with 1/sqrt(7)'s along the main diagonal, and 1's along the superdiagonal and the subdiagonal. [John M. Campbell,Jul 08 2011]
FORMULA
G.f.: (1-8x)/(1-15x+49x^2).
a(n) = Sum_{k=0..n}A165253(n,k)*7^(n-k).
a(n) = ((29-sqrt(29))*(15+sqrt(29))^n+(29+sqrt(29))*(15-sqrt(29))^n )/(58*2^n). [Klaus Brockhaus,Sep 26 2009]
MATHEMATICA
LinearRecurrence[{15, -49}, {1, 7}, 20] (*Harvey P. Dale,Jun 04 2021 *)
KEYWORD
nonn
AUTHOR
Philippe Deléham,Sep 14 2009
STATUS
approved