A126641 a(n) is the number of 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, at least one of digits 6,7 and at least one of digits 8,9.

9, 73, 537, 3625, 22809, 135913, 777177, 4308265, 23329689, 124104553, 651267417, 3382100905, 17421964569, 89180975593, 454265623257, 2304999893545, 11660373751449, 58845428989033, 296407578308697, 1490778208598185, 7488908074594329, 37584775814704873

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) = 16*5^n-32*4^n+24*3^n-8*2^n+1.

G.f.: -x*(120*x^4-250*x^3+207*x^2-62*x+9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Feb 22 2015

Maple

f:=n->16*5^n-32*4^n+24*3^n-8*2^n+1;

Prog

(PARI) Vec(-x*(120*x^4-250*x^3+207*x^2-62*x+9) / ((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: A143571 A244202 A079927 * A346229 A081627 A164588

Adjacent sequences: A126638 A126639 A126640 * A126642 A126643 A126644

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved