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

1,1

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).

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

Example

a(8) = 16595776.

Maple

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

Prog

(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

Crossrefs

Cf. A125630.

Sequence in context: A269655 A250360 A190130 * A206454 A001018 A097682

Adjacent sequences: A125905 A125906 A125907 * A125909 A125910 A125911

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Status

approved