A126639 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1,2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.

7, 49, 331, 2137, 13147, 77449, 440251, 2432857, 13151707, 69895849, 366600571, 1903222777, 9802234267, 50171448649, 255545887291, 1296626911897, 6559153748827, 33101134543849, 166731005404411, 838567970940217, 4212526479343387, 21141483461069449

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 (15,-85,225,-274,120).

Formula

a(n) = 9*5^n-18*4^n+15*3^n-6*2^n+1.

G.f.: -x*(120*x^4-238*x^3+191*x^2-56*x+7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Feb 22 2015

Maple

f:=n->9*5^n-18*4^n+15*3^n-6*2^n+1;

Mathematica

LinearRecurrence[{15, -85, 225, -274, 120}, {7, 49, 331, 2137, 13147}, 30] (* Harvey P. Dale, Aug 12 2015 *)

Prog

(PARI) Vec(-x*(120*x^4-238*x^3+191*x^2-56*x+7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Crossrefs

Cf. A125630, A125948, A125947, A125946, A125945, A125940, A125909, A125908, A125880, A125897, A125904, A125858.

Sequence in context: A267230 A188868 A267469 * A268942 A269638 A269535

Adjacent sequences: A126636 A126637 A126638 * A126640 A126641 A126642

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved