A125910 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 and at least one of digits 5,6,7,8,9.

9, 81, 723, 6381, 55539, 475461, 3993243, 32857101, 264890019, 2094889941, 16282118763, 124625344221, 941303216499, 7029057066021, 51980086628283, 381227207181741, 2776407821318979, 20100192515299701, 144786930345697803, 1038495372200033661

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) = 15*7^n-45*6^n+65*5^n-55*4^n+28*3^n-8*2^n+1.

G.f.: -3*x*(1680*x^6 -3976*x^5 +3946*x^4 -1807*x^3 +451*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) = 32857101.

Maple

f:=n->15*7^n-45*6^n+65*5^n-55*4^n+28*3^n-8*2^n+1;

Prog

(PARI) Vec(-3*x*(1680*x^6 -3976*x^5 +3946*x^4 -1807*x^3 +451*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: A206857 A073531 A206694 * A171283 A174108 A254435

Adjacent sequences: A125907 A125908 A125909 * A125911 A125912 A125913

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Status

approved