This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105281 #39 Mar 18 2025 07:35:43 %S A105281 0,6,42,258,1554,9330,55986,335922,2015538,12093234,72559410, %T A105281 435356466,2612138802,15672832818,94036996914,564221981490, %U A105281 3385331888946,20311991333682,121871948002098,731231688012594,4387390128075570,26324340768453426,157946044610720562 %N A105281 a(0)=0; a(n) = 6*a(n-1) + 6. %C A105281 Number of integers from 0 to (10^n) - 1 that lack 0, 1, 2 and 3 as a digit. %C A105281 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 %H A105281 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6). %F A105281 a(n) = 6^n + a(n-1) (with a(0)=0). - _Vincenzo Librandi_, Nov 13 2010 %F A105281 From _Colin Barker_, Jan 28 2013: (Start) %F A105281 a(n) = 7*a(n-1) - 6*a(n-2). %F A105281 G.f.: 6*x/((x-1)*(6*x-1)). (End) %F A105281 From _Elmo R. Oliveira_, Mar 16 2025: (Start) %F A105281 E.g.f.: 6*exp(x)*(exp(5*x) - 1)/5. %F A105281 a(n) = 6*(6^n - 1)/5. %F A105281 a(n) = 6*A003464(n). (End) %p A105281 a:=n->add(6^j,j=1..n): seq(a(n),n=0..30); # _Zerinvary Lajos_, Oct 03 2007 %t A105281 NestList[6#+6&,0,30] (* _Harvey P. Dale_, Jul 24 2012 *) %o A105281 (PARI) a(n)=if(n<0,0, (6^n-1)*6/5) %Y A105281 Cf. A000918, A003464, A029858, A052379, A052386, A080674. %Y A105281 Row n=6 of A228275. %K A105281 easy,nonn %O A105281 0,2 %A A105281 _Alexandre Wajnberg_, Apr 25 2005 %E A105281 More terms from _Harvey P. Dale_, Jul 24 2012