A105281 - OEIS

A105281

a(0)=0; a(n)=6*a(n-1)+6.

0, 6, 42, 258, 1554, 9330, 55986, 335922, 2015538, 12093234, 72559410, 435356466, 2612138802, 15672832818, 94036996914, 564221981490, 3385331888946, 20311991333682, 121871948002098, 731231688012594, 4387390128075570, 26324340768453426, 157946044610720562

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OFFSET

0,2

COMMENTS

Number of integers from 0 to (10^n)-1 that lack 0, 1, 2 and 3 as a digit.

Also, a(n) is the expected number of tosses of a single die needed to obtain for the first time a string of n consecutive 6's. - Jean M. Morales, Aug 04 2012

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (7,-6).

FORMULA

a(n) = 6^n+a(n-1) (with a(0)=0). - Vincenzo Librandi, Nov 13 2010

a(n) = 7*a(n-1)-6*a(n-2). G.f.: 6*x/((x-1)*(6*x-1)). - Colin Barker, Jan 28 2013

MAPLE

a:=n->add(6^j, j=1..n): seq(a(n), n=0..30); # Zerinvary Lajos, Oct 03 2007

MATHEMATICA

NestList[6#+6&, 0, 30] (* Harvey P. Dale, Jul 24 2012 *)

PROG

(PARI) a(n)=if(n<0, 0, (6^n-1)*6/5)