A126640 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and 2, at least one of digits 3,4, at least one of digits 5,6 and at least one of digits 7,8,9.

8, 60, 422, 2784, 17318, 102600, 584942, 3237504, 17516438, 93136440, 488625662, 2537103024, 13068059558, 66890498280, 340713533582, 1728792901344, 8745409322678, 44134458900120, 222306845468702, 1118087142184464, 5616691514201798, 28188613237893960

Offset: 1

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Keywords

• nonn
• base
• easy

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 (15,-85,225,-274,120).

Crossrefs

Cf. A125630, A125948, A125947, A125946, A125945, A125940, A125909, A125908, A125880, A125897, A125904, A125858.

Programs

Maple

f:=n->12*5^n-24*4^n+19*3^n-7*2^n+1;

Mathematica

LinearRecurrence[{15,-85,225,-274,120},{8, 60, 422, 2784, 17318},22] (* James C. McMahon, Dec 26 2024 *)

PARI

Vec(-2*x*(60*x^4-123*x^3+101*x^2-30*x+4) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Formula

a(n) = 12*5^n-24*4^n+19*3^n-7*2^n+1.

G.f.: -2*x*(60*x^4-123*x^3+101*x^2-30*x+4) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Feb 22 2015