A125945 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 and at least one of digits 5,6,7,8,9.

10, 96, 892, 8076, 71500, 619236, 5241652, 43355436, 350740540, 2780210676, 21641505412, 165814383996, 1253254845580, 9362782430916, 69259450905172, 508062802935756, 3700662365318620, 26794126632247956, 193018363703408932, 1384505203965202716

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) = 20*7^n-60*6^n+85*5^n-70*4^n+34*3^n-9*2^n+1.

G.f.: -2*x*(2520*x^6 -6054*x^5 +6063*x^4 -2794*x^3 +712*x^2 -92*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->20*7^n-60*6^n+85*5^n-70*4^n+34*3^n-9*2^n+1;

Prog

(PARI) a(n)=20*7^n-60*6^n+85*5^n-70*4^n+34*3^n-9*2^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A125630.

Sequence in context: A197083 A197086 A278359 * A259497 A190986 A287831

Adjacent sequences: A125942 A125943 A125944 * A125946 A125947 A125948

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Status

approved