A126643 - OEIS

%I #13 Sep 12 2023 15:29:00

%S 6,34,180,886,4116,18334,79260,335446,1398276,5765134,23581740,

%T 95900806,388345236,1567647934,6313474620,25382710966,101917608996,

%U 408831386734,1638809709900,6565693949926,26294146373556,105270707701534,421365218399580

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

%H Colin Barker, <a href="/A126643/b126643.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_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).

%F a(n) = 6*4^n-9*3^n+5*2^n-1.

%F a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - _Colin Barker_, Feb 22 2015

%F G.f.: -2*x*(12*x^3-25*x^2+13*x-3) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - _Colin Barker_, Feb 22 2015

%p f:=n->6*4^n-9*3^n+5*2^n-1;

%t LinearRecurrence[{10,-35,50,-24},{6,34,180,886},30] (* _Harvey P. Dale_, Sep 12 2023 *)

%o (PARI) Vec(-2*x*(12*x^3-25*x^2+13*x-3) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015

%Y Cf. A125630, A125948, A125947, A125946, A125945, A125940, A125909, A125908, A125880, A125897, A125904, A125858.

%K nonn,base,easy

%O 1,1

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