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

1,1

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).

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

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 *)

Prog

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

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.

Sequence in context: A244200 A334241 A079925 * A346227 A081896 A363413

Adjacent sequences: A126715 A126716 A126717 * A126719 A126720 A126721

Keyword

base,nonn,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 13 2007

Status

approved