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

Author

Alexandre Wajnberg, Apr 25 2005

Keywords

• easy
• nonn

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

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

Crossrefs

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

Row n=6 of A228275.

Programs

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 *)

PARI

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

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)

Extensions

More terms from Harvey P. Dale, Jul 24 2012