A165322 a(0)=1, a(1)=7, a(n)=15*a(n-1)-49*a(n-2) for n>1.

1, 7, 56, 497, 4711, 46312, 463841, 4688327, 47596696, 484222417, 4931098151, 50239573832, 511969798081, 5217807853447, 53180597695736, 542036380617137, 5524696422165991, 56310663682250152, 573949830547618721

Offset: 0

Author

Philippe Deléham, Sep 14 2009

Keywords

• nonn

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]

Links

• Index entries for linear recurrences with constant coefficients, signature (15,-49).

Crossrefs

Cf. A165253.

Programs

Mathematica

LinearRecurrence[{15,-49},{1,7},20] (* Harvey P. Dale, Jun 04 2021 *)

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]