A163412 a(n) = 12*a(n-1) - 34*a(n-2) for n>1, a(0)=1, a(1)=10.
1, 10, 86, 692, 5380, 41032, 309464, 2318480, 17299984, 128771488, 957058400, 7106470208, 52737656896, 391231895680, 2901702413696, 21518544511232, 159564652069120, 1183145311447552, 8772545567020544, 65043606215029760
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (12,-34).
Programs
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Magma
[n le 2 select 9*n-8 else 12*Self(n-1)-34*Self(n-2): n in [1..20]];
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Mathematica
LinearRecurrence[{12,-34}, {1,10}, 50] (* G. C. Greubel, Dec 21 2016 *) -
PARI
Vec((1-2*x)/(1-12*x+34*x^2) + O(x^50)) \\ G. C. Greubel, Dec 21 2016
Formula
a(n) = ((1+2*sqrt(2))*(6+sqrt(2))^n + (1-2*sqrt(2))*(6-sqrt(2))^n)/2.
O.g.f.: (1 - 2*x)/(1 - 12*x + 34*x^2).
E.g.f.: exp(6*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 21 2016
Comments