A125897 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 the digits 1,2,3 and at least one of the digits 4,5,6,7,8,9.

10, 100, 994, 9796, 95650, 924820, 8845714, 83575396, 778945090, 7156197940, 64800104434, 578648865796, 5100362368930, 44424892053460, 382839350691154, 3268062540952996, 27665402010407170, 232490197792427380, 1941315874498269874

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 (36,-546,4536,-22449,67284,-118124,109584,-40320).

Formula

a(n) = 18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1.

G.f.: -2*x*(20160*x^7 -54792*x^6 +53344*x^5 -28304*x^4 +8374*x^3 -1427*x^2 +130*x -5) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)). - Colin Barker, Feb 23 2015

Maple

f:=n->18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1;

Mathematica

Table[18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1, {n, 19}]  (* James C. McMahon, Dec 22 2024 *)

Prog

(PARI) vector(100, n, 18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1) \\ Colin Barker, Feb 23 2015

Crossrefs

Cf. A125630.

Sequence in context: A121084 A272501 A171284 * A395656 A182979 A355892

Adjacent sequences: A125894 A125895 A125896 * A125898 A125899 A125900

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 03 2007

Status

approved