A125946 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 digits 1,2, at least one of digits 3,4,5 and at least one of digits 6,7,8,9.

10, 98, 940, 8798, 80140, 709238, 6096100, 50950718, 415060060, 3305238278, 25807024660, 198131841038, 1499550640780, 11213044626518, 82997777543620, 609099122145758, 4437879770746300, 32138240678881958, 231547934781860980, 1661033550903240878

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 (28,-322,1960,-6769,13132,-13068,5040).

Formula

a(n) = 24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1.

G.f.: -2*x*(2520*x^6 -6042*x^5 +6043*x^4 -2783*x^3 +708*x^2 -91*x +5) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Feb 23 2015

Maple

f:=n->24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1;

Mathematica

Table[24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1, {n, 20}]  (* James C. McMahon, Dec 22 2024 *)

Prog

(PARI) vector(100, n, 24*7^n-72*6^n+98*5^n-76*4^n+35*3^n-9*2^n+1) \\ Colin Barker, Feb 23 2015

Crossrefs

Cf. A125630.

Sequence in context: A363186 A264462 A198968 * A158513 A125880 A125445

Adjacent sequences: A125943 A125944 A125945 * A125947 A125948 A125949

Keyword

nonn,base,easy,changed

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Status

approved