A163067 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 2, a(1) = 19.
2, 19, 178, 1656, 15352, 142064, 1313408, 12136896, 112126592, 1035748864, 9566914048, 88363846656, 816149635072, 7538085638144, 69622614990848, 643040841793536, 5939176725512192, 54854677118255104, 506641703733035008
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 (14,-44).
Programs
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Magma
[ n le 2 select 17*n-15 else 14*Self(n-1)-44*Self(n-2): n in [1..20] ];
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Mathematica
CoefficientList[Series[(2-9*x)/(1-14*x+44*x^2), {x,0,50}],x] (* or *) LinearRecurrence[{14,-44}, {2,19}, 30] (* G. C. Greubel, Dec 22 2017 *) -
PARI
x='x+O('x^30); Vec((2-9*x)/(1-14*x+44*x^2)) \\ G. C. Greubel, Dec 22 2017
Formula
a(n) = ((2+sqrt(5))*(7+sqrt(5))^n+(2-sqrt(5))*(7-sqrt(5))^n)/2.
G.f.: (2-9*x)/(1-14*x+44*x^2).
Comments