A125909 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of the digits 2,3 and at least one of digits 4,5,6,7,8,9.

9, 79, 681, 5791, 48729, 405919, 3340521, 27094111, 216288249, 1699187359, 13147825161, 100334472031, 756309350169, 5639967562399, 41669245538601, 305413957523551, 2223312590034489, 16091187568891039, 115885120813664841, 831075819022712671, 5938826569734181209

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) = 12*7^n-36*6^n+55*5^n-50*4^n+27*3^n-8*2^n+1.

G.f.: -x*(5040*x^6 -11988*x^5 +11944*x^4 -5479*x^3 +1367*x^2 -173*x+9) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Feb 22 2015

Maple

f:=n->12*7^n-36*6^n+55*5^n-50*4^n+27*3^n-8*2^n+1;

Mathematica

A125909[n_] := 12*7^n - 36*6^n + 55*5^n - 50*4^n + 27*3^n - 8*2^n + 1;
Array[A125909, 25] (* Paolo Xausa, May 06 2026 *)

Prog

(PARI) Vec(-x*(5040*x^6 -11988*x^5 +11944*x^4 -5479*x^3 +1367*x^2 -173*x+9) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Crossrefs

Cf. A125630.

Sequence in context: A198857 A126632 A294344 * A125421 A163445 A388414

Adjacent sequences: A125906 A125907 A125908 * A125910 A125911 A125912

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 04 2007

Status

approved