A163460 a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
1, 9, 82, 754, 6980, 64932, 606152, 5672648, 53180944, 499190928, 4689836320, 44087543584, 414630845504, 3900665825856, 36703540792448, 345415371476096, 3251026414485760, 30600669600254208, 288047075905950208
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (16, -62).
Programs
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Magma
[ n le 2 select 8*n-7 else 16*Self(n-1)-62*Self(n-2): n in [1..19] ];
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Mathematica
LinearRecurrence[{16,-62},{1,9},30] (* Harvey P. Dale, Jul 13 2014 *) -
PARI
Vec((1-7*x)/(1-16*x+62*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016
Formula
a(n) = ((2+sqrt(2))*(8+sqrt(2))^n + (2-sqrt(2))*(8-sqrt(2))^n)/4.
G.f.: (1-7*x)/(1-16*x+62*x^2).
E.g.f.: (1/2)*exp(8*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)). - G. C. Greubel, Dec 24 2016
Comments