A126627 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks digits 1,2,3 and at least one of digits 4,5,6,7,8,9.

7, 49, 343, 2401, 16807, 116929, 803383, 5432161, 36120007, 236404609, 1525601623, 9726181921, 61371928807, 383929313089, 2384606035063, 14723095123681, 90457525939207, 553507860826369, 3375536272503703, 20528377102849441, 124556950506727207

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) = 6*6^n-15*5^n+20*4^n-15*3^n+6*2^n-1.

G.f.: -x*(720*x^5 -1764*x^4 +1372*x^3 -539*x^2 +98*x -7) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Feb 23 2015

Maple

f:=n->6*6^n-15*5^n+20*4^n-15*3^n+6*2^n-1;

Mathematica

LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {7, 49, 343, 2401, 16807, 116929}, 30] (* Harvey P. Dale, Aug 02 2017 *)

Prog

(PARI) vector(100, n, 6*6^n-15*5^n+20*4^n-15*3^n+6*2^n-1) \\ Colin Barker, Feb 23 2015

Crossrefs

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

Sequence in context: A216130 A124536 A045578 * A206453 A000420 A050737

Adjacent sequences: A126624 A126625 A126626 * A126628 A126629 A126630

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved