A165322 - OEIS

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

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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]

LINKS

Table of n, a(n) for n=0..18.

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

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 *)

CROSSREFS

Cf. A165253.

Sequence in context: A145302 A233669 A265233 * A082305 A144263 A001730

Adjacent sequences: A165319 A165320 A165321 * A165323 A165324 A165325

KEYWORD

nonn

AUTHOR

Philippe Deléham, Sep 14 2009

STATUS

approved