A126635 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.

7, 47, 307, 1943, 11827, 69287, 392707, 2166743, 11703187, 62168327, 325983907, 1692105143, 8714154547, 44600020967, 227161443907, 1152585909143, 5830444893907, 29423488811207, 148206112628707, 745396075770743, 3744474953809267, 18792450661083047

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) = 8*5^n-16*4^n+14*3^n-6*2^n+1.

G.f.: -x*(120*x^4-242*x^3+197*x^2-58*x+7) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Feb 22 2015

Maple

f:=n->8*5^n-16*4^n+14*3^n-6*2^n+1;

Mathematica

LinearRecurrence[{15, -85, 225, -274, 120}, {7, 47, 307, 1943, 11827}, 30] (* Harvey P. Dale, Dec 31 2021 *)

Prog

(PARI) Vec(-x*(120*x^4-242*x^3+197*x^2-58*x+7) / ((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, A125910, A125909, A125908, A125880, A125897, A125904, A125858.

Sequence in context: A198845 A323131 A229010 * A085352 A125370 A163346

Adjacent sequences: A126632 A126633 A126634 * A126636 A126637 A126638

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved