Search: id:A023001
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%I A023001
%S A023001 0,1,9,73,585,4681,37449,299593,2396745,19173961,153391689,1227133513,
%T A023001 9817068105,78536544841,628292358729,5026338869833,40210710958665,
%U A023001 321685687669321,2573485501354569,20587884010836553,164703072086692425
%N A023001 (8^n - 1)/7.
%C A023001 Gives the (zero-based) positions of odd terms in A007556 (Mod[A007556[A0023001(n)],
               2]=1). - Farideh_Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Jun 
               13 2003
%C A023001 a(n) = A033138(3n-2). - Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), 
               May 31 2005
%C A023001 {1, 9, 73, 585, 4681, ...} is the binomial transform of A003950 . - Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Jul 22 2005
%C A023001 Except for the first term, a(n)=8*a(n-1)+1 (with a(1)=1) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]
%H A023001 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A023001 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Repunit.html">Link to a section of The World of Mathematics.</a>
%F A023001 Also sum of cubes of divisors of 2^(n-1): a(n)=A001158[A000079(n-1)] 
               - Labos E. (labos(AT)ana.sote.hu), Apr 10 2003 and Farideh_Firoozbakht 
               (f.firoozbakht(AT)sci.ui.ac.ir), Jun 13 2003
%F A023001 a(0)=0, a(n)=8*a(n-1)+1 for n>0 . G.f.:x/((1-8x)*(1-x)) - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 12 2006
%e A023001 Octal.............decimal (comment from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 14 2007):
%e A023001 0....................0
%e A023001 1....................1
%e A023001 11...................9
%e A023001 111.................73
%e A023001 1111...............585
%e A023001 11111.............4681
%e A023001 111111...........37449
%e A023001 1111111.........299593
%e A023001 11111111.......2396745
%e A023001 111111111.....19173961
%e A023001 1111111111...153391689
%e A023001 etc. ...............etc.
%p A023001 a:=n->sum(8^(n-j),j=1..n): seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 04 2007
%t A023001 Table[(8^n-1)/7, {n, 0, m}]
%o A023001 (Other) sage: [lucas_number1(n,9,8) for n in xrange(0, 21)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
%o A023001 (Other) sage: [gaussian_binomial(n,1,8) for n in xrange(0,21)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
%Y A023001 Cf. A007556.
%Y A023001 Sequence in context: A126641 A081627 A164588 this_sequence A015454 A121246 
               A086226
%Y A023001 Adjacent sequences: A022998 A022999 A023000 this_sequence A023002 A023003 
               A023004
%K A023001 easy,nonn
%O A023001 0,3
%A A023001 David W. Wilson (davidwwilson(AT)comcast.net)

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