A126628 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks digits 1 and 2, at least one of digits 3,4 and at least one of digits 5,6,7,8,9.

8, 62, 470, 3506, 25718, 184682, 1294910, 8867186, 59423078, 390804602, 2529567950, 16157024066, 102070798838, 639011269322, 3970835898590, 24524390352146, 150705922308998, 922285972770842, 5624983337550830, 34210314230099426, 207580309651649558

Offset: 1

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Keywords

• nonn
• base
• easy

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).

Crossrefs

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

Programs

Maple

f:=n->10*6^n-25*5^n+30*4^n-20*3^n+7*2^n-1;

Mathematica

CoefficientList[Series[-2*(360*x^5 - 882*x^4 + 697*x^3 - 284*x^2 + 53*x - 4)/((x - 1)*(2*x - 1)*(3*x - 1)*(4*x - 1)*(5*x - 1)*(6*x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 22 2022 *)

PARI

vector(100, n, 10*6^n-25*5^n+30*4^n-20*3^n+7*2^n-1) \\ Colin Barker, Feb 23 2015

Formula

a(n) = 10*6^n-25*5^n+30*4^n-20*3^n+7*2^n-1.

G.f.: -2*x*(360*x^5 -882*x^4 +697*x^3 -284*x^2 +53*x -4) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Feb 23 2015

a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - Wesley Ivan Hurt, Jun 22 2022