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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 and at least one of digits 5,6,7,8,9.
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%I #11 Jun 22 2022 11:48:13

%S 8,62,470,3506,25718,184682,1294910,8867186,59423078,390804602,

%T 2529567950,16157024066,102070798838,639011269322,3970835898590,

%U 24524390352146,150705922308998,922285972770842,5624983337550830,34210314230099426,207580309651649558

%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 and at least one of digits 5,6,7,8,9.

%H Colin Barker, <a href="/A126628/b126628.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) = 10*6^n-25*5^n+30*4^n-20*3^n+7*2^n-1.

%F G.f.: -2*x*(360*x^5 -882*x^4 +697*x^3 -284*x^2 +53*x -4) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - _Colin Barker_, Feb 23 2015

%F a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - _Wesley Ivan Hurt_, Jun 22 2022

%p f:=n->10*6^n-25*5^n+30*4^n-20*3^n+7*2^n-1;

%t CoefficientList[Series[-2*(360*x^5 - 882*x^4 + 697*x^3 - 284*x^2 + 53*x - 4)/((x - 1)*(2*x - 1)*(3*x - 1)*(4*x - 1)*(5*x - 1)*(6*x - 1)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jun 22 2022 *)

%o (PARI) vector(100, n, 10*6^n-25*5^n+30*4^n-20*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