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

1,1

Links

Table of n, a(n) for n=1..19.

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).

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

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 *)

Crossrefs

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

Sequence in context: A050793 A281203 A369335 * A125422 A190988 A287830

Adjacent sequences: A126630 A126631 A126632 * A126634 A126635 A126636

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved