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

1,1

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) = 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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A144143 A284225 A229011 * A085353 A125396 A163444

Adjacent sequences: A126625 A126626 A126627 * A126629 A126630 A126631

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved