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URL: https://oeis.org/A126631

⇱ A126631 - OEIS

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A126631
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 and at least one of digits 6,7,8,9.
3
9, 77, 633, 5021, 38409, 283277, 2019033, 13963901, 94144809, 621444077, 4031587833, 25787305181, 163054382409, 1021372934477, 6349128459033, 39222102764861, 241061530639209, 1475385002210477, 8998880800344633, 54732125638998941
OFFSET
1,1
FORMULA
a(n) = 16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1.
G.f.: -x*(720*x^5-1764*x^4+1412*x^3-591*x^2+112*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Feb 22 2015
EXAMPLE
a(8) = 13963901.
MAPLE
f:=n->16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1;
MATHEMATICA
LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {9, 77, 633, 5021, 38409, 283277}, 30] (* Harvey P. Dale, Oct 14 2016 *)
PROG
(PARI) Vec(-x*(720*x^5-1764*x^4+1412*x^3-591*x^2+112*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
KEYWORD
nonn,base,easy
AUTHOR
Aleksandar M. Janjic and Milan Janjic, Feb 08 2007
STATUS
approved