A125948 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 1,2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.

10, 100, 982, 9388, 86950, 778780, 6748822, 56713708, 463661830, 3700940860, 28941318262, 222422713228, 1684544507110, 12602134130140, 93308618633302, 684912371803948, 4990975002030790, 36147245625290620, 260449744313893942

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) = 27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1.

G.f.: -2*x*(2520*x^6 -6012*x^5 +5990*x^4 -2754*x^3 +701*x^2 -90*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->27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1;

Mathematica

Table[27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1, {n, 19}] (* James C. McMahon, Dec 23 2024 *)

Prog

(PARI) vector(100, n, 27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1) \\ Colin Barker, Feb 23 2015

Crossrefs

Cf. A125630.

Sequence in context: A231163 A136858 A334612 * A121084 A272501 A171284

Adjacent sequences: A125945 A125946 A125947 * A125949 A125950 A125951

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Status

approved