A125897 - OEIS

%I #15 Dec 22 2024 21:33:02

%S 10,100,994,9796,95650,924820,8845714,83575396,778945090,7156197940,

%T 64800104434,578648865796,5100362368930,44424892053460,

%U 382839350691154,3268062540952996,27665402010407170,232490197792427380,1941315874498269874

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

%H Colin Barker, <a href="/A125897/b125897.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (36,-546,4536,-22449,67284,-118124,109584,-40320).

%F a(n) = 18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1.

%F G.f.: -2*x*(20160*x^7 -54792*x^6 +53344*x^5 -28304*x^4 +8374*x^3 -1427*x^2 +130*x -5) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)). - _Colin Barker_, Feb 23 2015

%p f:=n->18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1;

%t Table[18*8^n-63*7^n+111*6^n-120*5^n+83*4^n-36*3^n+9*2^n-1, {n, 19}]  (* _James C. McMahon_, Dec 22 2024 *)

%o (PARI) vector(100, n, 18*8^n-63*7^n+111*6^n-120*5^n+83*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 03 2007