OFFSET
0,1
COMMENTS
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
LINKS
Colin Barker, Table of n, a(n) for n = 0..700
Index entries for linear recurrences with constant coefficients, signature (30,-125).
FORMULA
a(n) = ((5^n)/2)*(5^(n+2) - 5^n - 4), n >= 0.
From Colin Barker, Sep 12 2017: (Start)
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)
EXAMPLE
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.
MAPLE
a:= unapply(sum(i, i=5^n..5^(n+1)-1), n):
seq(a(n), n=0..20); # Alois P. Heinz, Sep 25 2017
PROG
(PARI) Vec(10*(1 - x) / ((1 - 5*x)*(1 - 25*x)) + O(x^30)) \\ Colin Barker, Sep 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Aug 28 2017
STATUS
approved