A126629 - OEIS

%I #11 Sep 26 2019 10:44:41

%S 8,64,506,3916,29498,215524,1527506,10528876,70841738,467044084,

%T 3027621506,19356463036,122355512378,766290978244,4762898595506,

%U 29420807536396,180813134269418,1106606890266004,6749433735297506,41050188511748956,249087606867080858

%N 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.

%H Colin Barker, <a href="/A126629/b126629.txt">Table of n, a(n) for n = 1..1000</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,-175,735,-1624,1764,-720).

%F a(n) = 12*6^n-30*5^n+34*4^n-21*3^n+7*2^n-1.

%F 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

%p f:=n->12*6^n-30*5^n+34*4^n-21*3^n+7*2^n-1;

%t LinearRecurrence[{21,-175,735,-1624,1764,-720},{8,64,506,3916,29498,215524},30] (* _Harvey P. Dale_, Sep 26 2019 *)

%o (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

%Y Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.

%K nonn,base,easy

%O 1,1

%A Aleksandar M. Janjic and _Milan Janjic_, Feb 08 2007