A126631 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.

9, 77, 633, 5021, 38409, 283277, 2019033, 13963901, 94144809, 621444077, 4031587833, 25787305181, 163054382409, 1021372934477, 6349128459033, 39222102764861, 241061530639209, 1475385002210477, 8998880800344633, 54732125638998941

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 (21,-175,735,-1624,1764,-720).

Formula

a(n) = 16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1.

G.f.: -x*(720*x^5-1764*x^4+1412*x^3-591*x^2+112*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Feb 22 2015

Example

a(8) = 13963901.

Maple

f:=n->16*6^n-40*5^n+44*4^n-26*3^n+8*2^n-1;

Mathematica

LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {9, 77, 633, 5021, 38409, 283277}, 30] (* Harvey P. Dale, Oct 14 2016 *)

Prog

(PARI) Vec(-x*(720*x^5-1764*x^4+1412*x^3-591*x^2+112*x-9)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015

Crossrefs

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

Sequence in context: A263471 A266125 A290708 * A190981 A254659 A346847

Adjacent sequences: A126628 A126629 A126630 * A126632 A126633 A126634

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved