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A163446
a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
3
1, 10, 98, 948, 9092, 86696, 823432, 7799760, 73743376, 696308896, 6568853024, 61930496832, 583619061824, 5498214185600, 51787045136512, 487703442676992, 4592458284368128, 43241719103916544, 407135092031840768
OFFSET
0,2
COMMENTS
Binomial transform of A163445. Inverse binomial transform of A163447.
FORMULA
a(n) = ((1+sqrt(2))*(8+sqrt(2))^n + (1-sqrt(2))*(8-sqrt(2))^n)/2.
G.f.: (1-6*x)/(1-16*x+62*x^2).
E.g.f.: exp(8*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016
MATHEMATICA
LinearRecurrence[{16, -62}, {1, 10}, 30] (* Harvey P. Dale, Sep 25 2015 *)
PROG
(Magma) [ n le 2 select 9*n-8 else 16*Self(n-1)-62*Self(n-2): n in [1..19] ];
(PARI) Vec((1-6*x)/(1-16*x+62*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016
CROSSREFS
Sequence in context: A158513 A125880 A125445 * A190869 A254599 A217634
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Jul 27 2009
STATUS
approved