A125948 - OEIS

%I #12 Jun 13 2015 00:52:18

%S 10,100,982,9388,86950,778780,6748822,56713708,463661830,3700940860,

%T 28941318262,222422713228,1684544507110,12602134130140,93308618633302,

%U 684912371803948,4990975002030790,36147245625290620,260449744313893942

%N 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.

%H Colin Barker, <a href="/A125948/b125948.txt">Table of n, a(n) for n = 1..1000</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (28,-322,1960,-6769,13132,-13068,5040).

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

%F 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

%p f:=n->27*7^n-81*6^n+108*5^n-81*4^n+36*3^n-9*2^n+1;

%o (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

%Y Cf. A125630.

%K nonn,base,easy

%O 1,1

%A Aleksandar M. Janjic and _Milan Janjic_, Feb 04 2007