

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.


3



7, 49, 343, 2401, 16807, 116929, 803383, 5432161, 36120007, 236404609, 1525601623, 9726181921, 61371928807, 383929313089, 2384606035063, 14723095123681, 90457525939207, 553507860826369, 3375536272503703, 20528377102849441, 124556950506727207
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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^n15*5^n+20*4^n15*3^n+6*2^n1.
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^n15*5^n+20*4^n15*3^n+6*2^n1;


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^n15*5^n+20*4^n15*3^n+6*2^n1) \\ 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



