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A125630 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and at least one of digits 2,3,4,5,6,7,8,9.

%I A125630 #15 Dec 20 2024 10:13:41
%S A125630 9,81,729,6561,59049,531441,4782969,43006401,385606089,3440214801,
%T A125630 30482931609,267934415841,2334817386729,20170171738161,
%U A125630 172797111134649,1468818073594881,12396189742824969,103943773544221521,866556801437680089,7187319207979903521
%N A125630 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and at least one of digits 2,3,4,5,6,7,8,9.
%C A125630 Note that the first seven terms of the sequence are powers of 9.
%H A125630 Colin Barker, <a href="/A125630/b125630.txt">Table of n, a(n) for n = 1..1000</a>
%H A125630 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A125630 <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 A125630 a(n) = 8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1.
%F A125630 G.f.: -9*x*(4480*x^7 -12176*x^6 +11772*x^5 -6168*x^4 +1809*x^3 -303*x^2 +27*x -1)/((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 22 2015
%e A125630 a(5) = 59049.
%p A125630 f:=n->8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1;
%t A125630 Table[8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1,{n,20}] (* _James C. McMahon_, Dec 20 2024 *)
%o A125630 (PARI) Vec(-9*x*(4480*x^7-12176*x^6+11772*x^5-6168*x^4+1809*x^3-303*x^2+27*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015
%K A125630 nonn,base,easy
%O A125630 1,1
%A A125630 Aleksandar M. Janjic and _Milan Janjic_, Jan 28 2007, Feb 13 2007