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A034474
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a(n) = 5^n + 1.
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58
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2, 6, 26, 126, 626, 3126, 15626, 78126, 390626, 1953126, 9765626, 48828126, 244140626, 1220703126, 6103515626, 30517578126, 152587890626, 762939453126, 3814697265626, 19073486328126, 95367431640626, 476837158203126
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 4 with a(0) = 2.
a(n) = 6*a(n-1) - 5*a(n-2) for n > 1.
G.f.: 1/(1-x) + 1/(1-5*x) = (2-6*x)/((1-x)*(1-5*x)).
E.g.f.: exp(x) + exp(5*x). (End)
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EXAMPLE
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G.f. = 2 + 6*x + 26*x^2 + 126*x^3 + 626*x^4 + 3126*x^5 + 15626*x^6 + ...
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MATHEMATICA
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Table[5^n + 1, {n, 0, 25}]
LinearRecurrence[{6, -5}, {2, 6}, 30] (* Harvey P. Dale, Jul 29 2015 *)
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PROG
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(Sage) [lucas_number2(n, 6, 5) for n in range(25)] # Zerinvary Lajos, Jul 08 2008
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CROSSREFS
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Cf. A000051, A000351, A007689, A024049, A033879, A034472, A034478, A034491, A034524, A052539, A062394, A062395, A062396, A062397, A063376, A063481, A074600-A074624, A178248, A228081, A279396.
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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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