login
A126632
a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.
3
9, 79, 669, 5431, 42189, 314119, 2251629, 15625591, 105563469, 697683559, 4529641389, 28986744151, 183339095949, 1148652643399, 7141191155949, 44118519949111, 271168742599629, 1659705919705639, 10123331198091309, 61571999920648471
OFFSET
1,1
FORMULA
a(n) = 18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1.
G.f.: -x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Feb 22 2015
EXAMPLE
a(8) = 15625591.
MAPLE
f:=n->18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1;
PROG
(PARI) Vec(-x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015
KEYWORD
nonn,base,easy
AUTHOR
Aleksandar M. Janjic and Milan Janjic, Feb 08 2007
STATUS
approved