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A163461
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a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
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3
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1, 10, 101, 1028, 10525, 108238, 1116809, 11551760, 119703769, 1242078802, 12900820685, 134090546972, 1394465011381, 14507216994070, 150967169994161, 1571338917363368, 16357694083001905, 170302719022328218
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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) = ((2+sqrt(2))*(9+sqrt(2))^n + (2-sqrt(2))*(9-sqrt(2))^n)/4.
G.f.: (1-8*x)/(1-18*x+79*x^2).
E.g.f.: (1/2)*exp(9*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)). - G. C. Greubel, Dec 24 2016
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MATHEMATICA
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LinearRecurrence[{18, -79}, {1, 10}, 30] (* Harvey P. Dale, Jul 25 2013 *)
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PROG
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(Magma) [ n le 2 select 9*n-8 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];
(PARI) Vec((1-8*x)/(1-18*x+79*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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