A126718 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5, at least one of digits 6,7 and at least one of digits 8,9.

7, 43, 235, 1171, 5467, 24403, 105595, 447091, 1864027, 7686163, 31440955, 127865011, 517788187, 2090186323, 8417944315, 33843570931, 135890057947, 545108340883, 2185079263675, 8754257900851, 35058860433307, 140360940805843, 561820285607035

Offset: 1

Author

Aleksandar M. Janjic and Milan Janjic, Feb 13 2007

Keywords

• base
• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Crossrefs

Cf. A125910, A125945, A125946, A125947, A125948, A125880, A125630, A125987, A125904, A125858, A125909, A125908, A126646, A126645, A126644, A126643, A126642, A126641, A126640, A126639, A126635, A126634, A126633, A126632, A126631, A126628, A126627.

Programs

Magma

[8*4^n-12*3^n+6*2^n-1: n in [1..30]]; // Vincenzo Librandi, May 31 2011

Maple

a:=n->8*4^n-12*3^n+6*2^n-1;

Mathematica

LinearRecurrence[{10,-35,50,-24},{7, 43, 235, 1171},23] (* James C. McMahon, Dec 27 2024 *)

PARI

Vec(-x*(24*x^3-50*x^2+27*x-7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Formula

a(n) = 8*4^n - 12*3^n + 6*2^n - 1.

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4). - Colin Barker, Feb 22 2015

G.f.: -x*(24*x^3 - 50*x^2 + 27*x - 7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Feb 22 2015