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A163448
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a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
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2
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1, 12, 142, 1664, 19364, 224208, 2586488, 29757376, 341671696, 3917211072, 44860395232, 513321219584, 5870105658944, 67096633659648, 766662318616448, 8757776273683456, 100022618249257216, 1142190290164165632
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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))*(10+sqrt(2))^n + (1-sqrt(2))*(10-sqrt(2))^n)/2.
G.f.: (1-8*x)/(1-20*x+98*x^2).
a(n) = (31*(10-sqrt(2))^n - 41*sqrt(2)*(10-sqrt(2))^n + 49*(10+sqrt(2))^n + 49*sqrt(2)*(10+sqrt(2))^n)/(98*(10+sqrt(2))). - Harvey P. Dale, Nov 14 2011
E.g.f.: exp(10*x)*( 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[{20, -98}, {1, 12}, 30] (* or *) With[{ms=10-Sqrt[2], ps=10+ Sqrt[2]}, Table[Simplify[(31ms^n-41Sqrt[2](ms^n)+49ps^n+49Sqrt[2] ps^n)/ (98ps)], {n, 20}]] (* Harvey P. Dale, Nov 14 2011 *)
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PROG
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(Magma) [ n le 2 select 11*n-10 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];
(PARI) Vec((1-8*x)/(1-20*x+98*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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