A126634 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.

6, 36, 216, 1296, 7656, 44136, 248016, 1362096, 7338456, 38927736, 203958816, 1058224896, 5448329256, 27880971336, 141993797616, 720419919696, 3644189320056, 18390164454936, 92630272564416, 465876904526496, 2340309918950856, 11745320884258536

Offset: 1

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Keywords

• nonn
• base
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).

Crossrefs

Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.

Programs

Maple

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

Mathematica

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

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

Formula

a(n) = 5*5^n-10*4^n+10*3^n-5*2^n+1.

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