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A165322
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a(0)=1, a(1)=7, a(n)=15*a(n-1)-49*a(n-2) for n>1.
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2
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1, 7, 56, 497, 4711, 46312, 463841, 4688327, 47596696, 484222417, 4931098151, 50239573832, 511969798081, 5217807853447, 53180597695736, 542036380617137, 5524696422165991, 56310663682250152, 573949830547618721
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OFFSET
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0,2
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COMMENTS
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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]
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LINKS
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FORMULA
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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]
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MATHEMATICA
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LinearRecurrence[{15, -49}, {1, 7}, 20] (* Harvey P. Dale, Jun 04 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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