A126643 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4, at least one of digits 5,6 and at least one of digits 7,8,9.

6, 34, 180, 886, 4116, 18334, 79260, 335446, 1398276, 5765134, 23581740, 95900806, 388345236, 1567647934, 6313474620, 25382710966, 101917608996, 408831386734, 1638809709900, 6565693949926, 26294146373556, 105270707701534, 421365218399580

Offset

1,1

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 (10,-35,50,-24).

Formula

a(n) = 6*4^n-9*3^n+5*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.: -2*x*(12*x^3-25*x^2+13*x-3) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Feb 22 2015

Maple

f:=n->6*4^n-9*3^n+5*2^n-1;

Mathematica

LinearRecurrence[{10, -35, 50, -24}, {6, 34, 180, 886}, 30] (* Harvey P. Dale, Sep 12 2023 *)

Prog

(PARI) Vec(-2*x*(12*x^3-25*x^2+13*x-3) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Crossrefs

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

Sequence in context: A198765 A274405 A144142 * A320745 A084775 A327740

Adjacent sequences: A126640 A126641 A126642 * A126644 A126645 A126646

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved