A162814 a(n) = 6*a(n-1)-6*a(n-2) for n > 1; a(0) = 5, a(1) = 18.
5, 18, 78, 360, 1692, 7992, 37800, 178848, 846288, 4004640, 18950112, 89672832, 424336320, 2007980928, 9501867648, 44963320320, 212768716032, 1006832374272, 4764381949440, 22545297451008, 106685493009408, 504841173350400
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (6,-6).
Programs
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Magma
[ n le 2 select 13*n-8 else 6*Self(n-1)-6*Self(n-2): n in [1..22] ];
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Mathematica
LinearRecurrence[{6,-6},{5,18},40] (* Harvey P. Dale, Mar 26 2022 *)
Formula
a(n) = ((5+sqrt(3))*(3+sqrt(3))^n+(5-sqrt(3))*(3-sqrt(3))^n)/2.
G.f.: (5-12*x)/(1-6*x+6*x^2).
Comments