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A291658
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a(n) is the sum of all integers from 5^n to 5^(n+1)-1.
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1
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10, 290, 7450, 187250, 4686250, 117181250, 2929656250, 73242031250, 1831053906250, 45776363281250, 1144409160156250, 28610229394531250, 715255736816406250, 17881393430175781250, 447034835803222656250, 11175870895324707031250, 279396772384338378906250
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OFFSET
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0,1
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COMMENTS
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a(n) is the sum of all (positive) numbers having exactly (n+1) digits when written in base 5. - Alois P. Heinz, Sep 25 2017
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LINKS
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FORMULA
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a(n) = ((5^n)/2)*(5^(n+2) - 5^n - 4), n >= 0.
G.f.: 10*(1 - x) / ((1 - 5*x)*(1 - 25*x)).
a(n) = 30*a(n-1) - 125*a(n-2) for n>1.
(End)
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EXAMPLE
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For n=0, the sum is from 1 to 4, so a(0)=10;
for n=1, the sum is from 5 to 24, so a(1)=290, etc.
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MAPLE
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a:= unapply(sum(i, i=5^n..5^(n+1)-1), n):
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PROG
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(PARI) Vec(10*(1 - x) / ((1 - 5*x)*(1 - 25*x)) + O(x^30)) \\ Colin Barker, Sep 12 2017
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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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