A126640 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and 2, at least one of digits 3,4, at least one of digits 5,6 and at least one of digits 7,8,9.

8, 60, 422, 2784, 17318, 102600, 584942, 3237504, 17516438, 93136440, 488625662, 2537103024, 13068059558, 66890498280, 340713533582, 1728792901344, 8745409322678, 44134458900120, 222306845468702, 1118087142184464, 5616691514201798, 28188613237893960

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) = 12*5^n-24*4^n+19*3^n-7*2^n+1.

G.f.: -2*x*(60*x^4-123*x^3+101*x^2-30*x+4) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Feb 22 2015

Maple

f:=n->12*5^n-24*4^n+19*3^n-7*2^n+1;

Mathematica

LinearRecurrence[{15, -85, 225, -274, 120}, {8, 60, 422, 2784, 17318}, 22] (* James C. McMahon, Dec 26 2024 *)

Prog

(PARI) Vec(-2*x*(60*x^4-123*x^3+101*x^2-30*x+4) / ((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: A081158 A002927 A274800 * A093132 A094169 A129325

Adjacent sequences: A126637 A126638 A126639 * A126641 A126642 A126643

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved