A125908 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1 and 2 and at least one of digits 3,4,5,6,7,8,9.

8, 64, 512, 4096, 32768, 262144, 2092112, 16595776, 130437728, 1013866624, 7788438512, 59145432256, 444357721088, 3306242197504, 24389881261712, 178578361769536, 1299058046034848, 9397253451942784, 67653687455953712, 485065987257543616

Offset: 1

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Keywords

• nonn
• base
• easy

Examples

			a(8) = 16595776.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).

Crossrefs

Cf. A125630.

Programs

Maple

f:=n->7*7^n-21*6^n+35*5^n-35*4^n+21*3^n-7*2^n+1;

PARI

Vec(-8*x*(630*x^6-1476*x^5+1457*x^4-664*x^3+162*x^2-20*x+1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Formula

a(n) = 7*7^n-21*6^n+35*5^n-35*4^n+21*3^n-7*2^n+1.

G.f.: -8*x*(630*x^6 -1476*x^5 +1457*x^4 -664*x^3 +162*x^2 -20*x +1)/((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Feb 22 2015