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A125630
a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and at least one of digits 2,3,4,5,6,7,8,9.
31
9, 81, 729, 6561, 59049, 531441, 4782969, 43006401, 385606089, 3440214801, 30482931609, 267934415841, 2334817386729, 20170171738161, 172797111134649, 1468818073594881, 12396189742824969, 103943773544221521, 866556801437680089, 7187319207979903521
OFFSET
1,1
COMMENTS
Note that the first seven terms of the sequence are powers of 9.
LINKS
FORMULA
a(n) = 8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1.
G.f.: -9*x*(4480*x^7 -12176*x^6 +11772*x^5 -6168*x^4 +1809*x^3 -303*x^2 +27*x -1)/((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)). - Colin Barker, Feb 22 2015
EXAMPLE
a(5) = 59049.
MAPLE
f:=n->8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1;
PROG
(PARI) Vec(-9*x*(4480*x^7-12176*x^6+11772*x^5-6168*x^4+1809*x^3-303*x^2+27*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015
CROSSREFS
Sequence in context: A228972 A125947 A120997 * A100062 A001019 A074118
KEYWORD
nonn,base,easy
AUTHOR
Aleksandar M. Janjic and Milan Janjic, Jan 28 2007, Feb 13 2007
STATUS
approved