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A163444
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a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
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2
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1, 8, 62, 472, 3556, 26624, 198584, 1477792, 10981648, 81534848, 605042144, 4488320896, 33288417856, 246858103808, 1830491038592, 13572716933632, 100635907891456, 746158518953984, 5532281359138304, 41017986665224192
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = ((1+sqrt(2))*(6+sqrt(2))^n + (1-sqrt(2))*(6-sqrt(2))^n)/2.
G.f.: (1-4*x)/(1-12*x+34*x^2).
E.g.f.: 2*exp(6*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016
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MATHEMATICA
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LinearRecurrence[{12, -34}, {1, 8}, 50] (* G. C. Greubel, Dec 23 2016 *)
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PROG
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(Magma) [ n le 2 select 7*n-6 else 12*Self(n-1)-34*Self(n-2): n in [1..20] ];
(PARI) Vec((1-4*x)/(1-12*x+34*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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