A126718 - OEIS

%I #24 Dec 27 2024 13:02:51

%S 7,43,235,1171,5467,24403,105595,447091,1864027,7686163,31440955,

%T 127865011,517788187,2090186323,8417944315,33843570931,135890057947,

%U 545108340883,2185079263675,8754257900851,35058860433307,140360940805843,561820285607035

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

%H Vincenzo Librandi, <a href="/A126718/b126718.txt">Table of n, a(n) for n = 1..200</a>

%H Milan Janjic, <a href="https://old.pmf.unibl.org/wp-content/uploads/2017/10/enumfun.pdf">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) = 8*4^n - 12*3^n + 6*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.: -x*(24*x^3 - 50*x^2 + 27*x - 7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - _Colin Barker_, Feb 22 2015

%p a:=n->8*4^n-12*3^n+6*2^n-1;

%t LinearRecurrence[{10,-35,50,-24},{7, 43, 235, 1171},23] (* _James C. McMahon_, Dec 27 2024 *)

%o (Magma) [8*4^n-12*3^n+6*2^n-1: n in [1..30]]; // _Vincenzo Librandi_, May 31 2011

%o (PARI) Vec(-x*(24*x^3-50*x^2+27*x-7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)) + O(x^100)) \\ _Colin Barker_, Feb 22 2015

%Y Cf. A125910, A125945, A125946, A125947, A125948, A125880, A125630, A125987, A125904, A125858, A125909, A125908, A126646, A126645, A126644, A126643, A126642, A126641, A126640, A126639, A126635, A126634, A126633, A126632, A126631, A126628, A126627.

%K base,nonn,easy

%O 1,1

%A Aleksandar M. Janjic and _Milan Janjic_, Feb 13 2007