A125947 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 2,3,4,5 and at least one of digits 6,7,8,9.

9, 81, 729, 6513, 57369, 495921, 4194969, 34689393, 280607769, 2224214961, 17313344409, 132651929073, 1002605145369, 7490229758001, 55407572177049, 406450276733553, 2960529995462169, 21435301615525041, 154414691892116889, 1107604165960750833

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) = 16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1.

G.f.: -3*x*(1680*x^6 -3988*x^5 +3968*x^4 -1819*x^3 +453*x^2-57*x+3) / ((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) = 34689393.

Maple

f:=n->16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1;

Mathematica

Table[ 16*7^n-48*6^n+68*5^n-56*4^n+28*3^n-8*2^n+1, {n, 20}] (* James C. McMahon, Dec 23 2024 *)

Prog

(PARI) Vec(-3*x*(1680*x^6 -3988*x^5 +3968*x^4 -1819*x^3 +453*x^2-57*x+3) / ((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: A267790 A268014 A228972 * A120997 A125630 A100062

Adjacent sequences: A125944 A125945 A125946 * A125948 A125949 A125950

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Status

approved