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

1,1

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).

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

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;

Prog

(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

Crossrefs

Cf. A125630.

Sequence in context: A358442 A136877 A257969 * A272502 A355894 A276596

Adjacent sequences: A125901 A125902 A125903 * A125905 A125906 A125907

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 03 2007

Status

approved