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

%I #13 Apr 01 2018 09:43:54

%S 6,36,216,1296,7656,44136,248016,1362096,7338456,38927736,203958816,

%T 1058224896,5448329256,27880971336,141993797616,720419919696,

%U 3644189320056,18390164454936,92630272564416,465876904526496,2340309918950856,11745320884258536

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

%H Colin Barker, <a href="/A126634/b126634.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) = 5*5^n-10*4^n+10*3^n-5*2^n+1.

%F G.f.: -6*x*(20*x^4-39*x^3+31*x^2-9*x+1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - _Colin Barker_, Feb 22 2015

%p f:=n->5*5^n-10*4^n+10*3^n-5*2^n+1;

%t LinearRecurrence[{15,-85,225,-274,120},{6,36,216,1296,7656},30] (* _Harvey P. Dale_, Apr 01 2018 *)

%o (PARI) Vec(-6*x*(20*x^4-39*x^3+31*x^2-9*x+1) / ((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