cp's OEIS Frontend

A126632 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 digits 2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.

%I A126632 #20 Dec 26 2024 19:52:01
%S A126632 9,79,669,5431,42189,314119,2251629,15625591,105563469,697683559,
%T A126632 4529641389,28986744151,183339095949,1148652643399,7141191155949,
%U A126632 44118519949111,271168742599629,1659705919705639,10123331198091309,61571999920648471
%N A126632 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 digits 2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.
%H A126632 Colin Barker, <a href="/A126632/b126632.txt">Table of n, a(n) for n = 1..1000</a>
%H A126632 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A126632 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,-175,735,-1624,1764,-720).
%F A126632 a(n) = 18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1.
%F A126632 G.f.: -x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - _Colin Barker_, Feb 22 2015
%e A126632 a(8) = 15625591.
%p A126632 f:=n->18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1;
%t A126632 LinearRecurrence[{21,-175,735,-1624,1764,-720},{9, 79, 669, 5431, 42189, 314119},20] (* _James C. McMahon_, Dec 26 2024 *)
%o A126632 (PARI) Vec(-x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015
%Y A126632 Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.
%K A126632 nonn,base,easy
%O A126632 1,1
%A A126632 Aleksandar M. Janjic and _Milan Janjic_, Feb 08 2007