A125880 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 and at least one of the digits 3,4,5,6,7,8,9.

10, 98, 946, 9026, 85330, 800738, 7463746, 69054146, 633214450, 5746812578, 51574432546, 457575310466, 4014480866770, 34850492651618, 299615359353346, 2553264555537986, 21587837904314290, 181256003521421858, 1512536914179602146, 12553861394003656706

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) = 14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1.

G.f.: -2*x*(20160*x^7 -54792*x^6 +53420*x^5 -28436*x^4 +8441*x^3 -1439*x^2 +131*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->14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1;

Mathematica

Table[14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1, {n, 20}] (* James C. McMahon, Dec 22 2024 *)

Prog

(PARI) vector(100, n, 14*8^n-49*7^n+91*6^n-105*5^n+77*4^n-35*3^n+9*2^n-1) \\ Colin Barker, Feb 23 2015

Crossrefs

Cf. A125630.

Sequence in context: A198968 A125946 A158513 * A125445 A163446 A190869

Adjacent sequences: A125877 A125878 A125879 * A125881 A125882 A125883

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 03 2007, Feb 13 2007

Status

approved