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A126629
a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks digits 1 and 2, at least one of digits 3,4,5 and at least one of digits 6,7,8,9.
2
8, 64, 506, 3916, 29498, 215524, 1527506, 10528876, 70841738, 467044084, 3027621506, 19356463036, 122355512378, 766290978244, 4762898595506, 29420807536396, 180813134269418, 1106606890266004, 6749433735297506, 41050188511748956, 249087606867080858
OFFSET
1,1
FORMULA
a(n) = 12*6^n-30*5^n+34*4^n-21*3^n+7*2^n-1.
G.f.: -2*x*(360*x^5 -882*x^4 +695*x^3 -281*x^2 +52*x -4) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Feb 23 2015
MAPLE
f:=n->12*6^n-30*5^n+34*4^n-21*3^n+7*2^n-1;
MATHEMATICA
LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {8, 64, 506, 3916, 29498, 215524}, 30] (* Harvey P. Dale, Sep 26 2019 *)
PROG
(PARI) vector(100, n, 12*6^n-30*5^n+34*4^n-21*3^n+7*2^n-1) \\ Colin Barker, Feb 23 2015
KEYWORD
nonn,base,easy
AUTHOR
Aleksandar M. Janjic and Milan Janjic, Feb 08 2007
STATUS
approved