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A005060
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a(n) = 5^n - 4^n.
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21
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0, 1, 9, 61, 369, 2101, 11529, 61741, 325089, 1690981, 8717049, 44633821, 227363409, 1153594261, 5835080169, 29443836301, 148292923329, 745759583941, 3745977788889, 18798608421181, 94267920012849
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OFFSET
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0,3
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COMMENTS
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Also, the number of numbers with at most n digits whose largest digit equals 4. - M. F. Hasler, May 03 2015
a(n) is divisible by 7 iff n is divisible by 6; for example: a(6) = 11529 = 7 * 1647 (see 'Les cahier du bac' or subtract A070365 and A153727 and locate zeros). - Bernard Schott, Oct 02 2020
a(n) is the number of n-digit numbers whose smallest decimal digit is 5. - Stefano Spezia, Nov 15 2023
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REFERENCES
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Les Cahiers du Bac, Terminales C & E, Tome 1, 1985, Exercice 109, p. 18; Bac Rouen, Série C, 1978.
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LINKS
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FORMULA
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a(n) = 5*a(n-1) + 4^(n-1). - Xavier Acloque, Oct 20 2003
G.f.: 1/(1-5*x) - 1/(1-4*x).
E.g.f.: e^(5*x) - e^(4*x). (End)
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MAPLE
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a:=n->sum(4^(n-j)*binomial(n, j), j=1..n): seq(a(n), n=0..18); # Zerinvary Lajos, Jan 04 2007
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MATHEMATICA
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LinearRecurrence[{9, -20}, {0, 1}, 30] (* Harvey P. Dale, Oct 01 2016 *)
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PROG
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(Sage) [lucas_number1(n, 9, 20) for n in range(21)] # Zerinvary Lajos, Apr 23 2009
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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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