A126634 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4 and at least one of digits 5,6,7,8,9.

6, 36, 216, 1296, 7656, 44136, 248016, 1362096, 7338456, 38927736, 203958816, 1058224896, 5448329256, 27880971336, 141993797616, 720419919696, 3644189320056, 18390164454936, 92630272564416, 465876904526496, 2340309918950856, 11745320884258536

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) = 5*5^n-10*4^n+10*3^n-5*2^n+1.

G.f.: -6*x*(20*x^4-39*x^3+31*x^2-9*x+1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Feb 22 2015

Maple

f:=n->5*5^n-10*4^n+10*3^n-5*2^n+1;

Mathematica

LinearRecurrence[{15, -85, 225, -274, 120}, {6, 36, 216, 1296, 7656}, 30] (* Harvey P. Dale, Apr 01 2018 *)

Prog

(PARI) Vec(-6*x*(20*x^4-39*x^3+31*x^2-9*x+1) / ((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: A269773 A269653 A250358 * A216128 A007275 A206452

Adjacent sequences: A126631 A126632 A126633 * A126635 A126636 A126637

Keyword

nonn,base,easy

Author

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007

Status

approved