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

Offset

0,2

Comments

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

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

From Colin Barker, Jan 28 2013: (Start)

a(n) = 7*a(n-1) - 6*a(n-2).

G.f.: 6*x/((x-1)*(6*x-1)). (End)

From Elmo R. Oliveira, Mar 16 2025: (Start)

E.g.f.: 6*exp(x)*(exp(5*x) - 1)/5.

a(n) = 6*(6^n - 1)/5.

a(n) = 6*A003464(n). (End)

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)

Crossrefs

Cf. A000918, A003464, A029858, A052379, A052386, A080674.

Row n=6 of A228275.

Sequence in context: A141834 A344065 A180355 * A246938 A158797 A218060

Adjacent sequences: A105278 A105279 A105280 * A105282 A105283 A105284

Keyword

easy,nonn

Author

Alexandre Wajnberg, Apr 25 2005

Extensions

More terms from Harvey P. Dale, Jul 24 2012

Status

approved