A126633 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks at least one of digits 1, 2, at least one of digits 3,4, at least one of digits 5,6 and at least one of digits 7,8,9.

10, 94, 832, 6946, 54880, 412714, 2975752, 20722306, 140285200, 928323034, 6031661272, 38617025266, 244322679520, 1531014308554, 9519483716392, 58816232361826, 361524350929840, 2212804949145274, 13497228660885112

Offset: 1

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Keywords

• nonn
• base
• easy

Links

• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).

Crossrefs

Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.

Programs

Maple

A126633:=n->24*6^n-60*5^n+62*4^n-33*3^n+9*2^n-1; seq(A126633(n), n=1..20);

Mathematica

Table[24*6^n - 60*5^n + 62*4^n - 33*3^n + 9*2^n - 1, {n, 20}] (* Wesley Ivan Hurt, May 03 2014 *)
LinearRecurrence[{21,-175,735,-1624,1764,-720},{10,94,832,6946,54880,412714},30] (* Harvey P. Dale, May 05 2018 *)

Formula

a(n) = 24*6^n-60*5^n+62*4^n-33*3^n+9*2^n-1.

G.f.: -2*x*(360*x^5-882*x^4+713*x^3-304*x^2+58*x-5) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, May 04 2014