login
a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.
3

%I #12 Dec 31 2021 13:28:41

%S 7,47,307,1943,11827,69287,392707,2166743,11703187,62168327,325983907,

%T 1692105143,8714154547,44600020967,227161443907,1152585909143,

%U 5830444893907,29423488811207,148206112628707,745396075770743,3744474953809267,18792450661083047

%N a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.

%H Colin Barker, <a href="/A126635/b126635.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_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).

%F a(n) = 8*5^n-16*4^n+14*3^n-6*2^n+1.

%F G.f.: -x*(120*x^4-242*x^3+197*x^2-58*x+7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - _Colin Barker_, Feb 22 2015

%p f:=n->8*5^n-16*4^n+14*3^n-6*2^n+1;

%t LinearRecurrence[{15,-85,225,-274,120},{7,47,307,1943,11827},30] (* _Harvey P. Dale_, Dec 31 2021 *)

%o (PARI) Vec(-x*(120*x^4-242*x^3+197*x^2-58*x+7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 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