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.
9, 81, 729, 6561, 59049, 531441, 4782969, 43006401, 385606089, 3440214801, 30482931609, 267934415841, 2334817386729, 20170171738161, 172797111134649, 1468818073594881, 12396189742824969, 103943773544221521, 866556801437680089, 7187319207979903521
Offset: 1
Examples
a(5) = 59049.
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 (36,-546,4536,-22449,67284,-118124,109584,-40320).
Programs
-
Maple
f:=n->8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1;
-
Mathematica
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 *) -
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
Formula
a(n) = 8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1.
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
Comments