A125904 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks at least one of the digits 1,2,3,4 and at least one of the digits 5,6,7,8,9.

10, 100, 1000, 9976, 98920, 971440, 9420400, 90005176, 846101080, 7822770880, 71163913600, 637585923976, 5633160763240, 49148451899920, 424055315011600, 3623013325068376, 30689130457473400, 258015134469182560, 2155143129458730400

Offset: 1

Author

Aleksandar M. Janjic and Milan Janjic, Feb 03 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 (36,-546,4536,-22449,67284,-118124,109584,-40320).

Crossrefs

Cf. A125630.

Programs

Maple

f:=n->20*8^n-70*7^n+120*6^n-125*5^n+84*4^n-36*3^n+9*2^n-1;

PARI

vector(100, n, 20*8^n-70*7^n+120*6^n-125*5^n+84*4^n-36*3^n+9*2^n-1) \\ Colin Barker, Feb 23 2015

Formula

a(n) = 20*8^n-70*7^n+120*6^n-125*5^n+84*4^n-36*3^n+9*2^n-1.

G.f.: -2*x*(20160*x^7 -54792*x^6 +53362*x^5 -28337*x^4 +8392*x^3 -1430*x^2 +130*x -5) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)). - Colin Barker, Feb 23 2015