A163472 a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 3, a(1) = 21.
3, 21, 153, 1143, 8667, 66285, 509409, 3925503, 30295539, 234004869, 1808305641, 13977507015, 108055998027, 835414244829, 6459123003057, 49940805957327, 386138612387043, 2985616752052725, 23084826815860281, 178492568972583447
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 (12,-33).
Programs
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Magma
[ n le 2 select 18*n-15 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];
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Mathematica
LinearRecurrence[{12, -33}, {3, 21}, 50] (* G. C. Greubel, Jul 26 2017 *) -
PARI
x='x+O('x^50); Vec((3-15*x)/(1-12*x+33*x^2)) \\ G. C. Greubel, Jul 26 2017
Formula
a(n) = ((3+sqrt(3))*(6+sqrt(3))^n + (3-sqrt(3))*(6-sqrt(3))^n)/2.
G.f.: (3-15*x)/(1-12*x+33*x^2).
E.g.f.: exp(6*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017
Comments