A126642 a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4 and 5 and at least one of digits 6,7,8,9.

5, 25, 125, 601, 2765, 12265, 52925, 223801, 932525, 3844105, 15722525, 63936601, 258902285, 1045109545, 4209004925, 16921851001, 67945160045, 272554432585, 1092540156125, 4377129999001, 17529432313805, 70180474597225, 280910151192125

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 (10,-35,50,-24).

Formula

a(n) = 4*4^n-6*3^n+4*2^n-1.

a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - Colin Barker, Feb 22 2015

G.f.: -x*(24*x^3-50*x^2+25*x-5) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Feb 22 2015

Maple

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

Prog

(PARI) Vec(-x*(24*x^3-50*x^2+25*x-5) / ((x-1)*(2*x-1)*(3*x-1)*(4*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: A366323 A267780 A228736 * A269615 A269579 A269431

Adjacent sequences: A126639 A126640 A126641 * A126643 A126644 A126645

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved