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0, 1, 9, 73, 585, 4681, 37449, 299593, 2396745, 19173961, 153391689, 1227133513, 9817068105, 78536544841, 628292358729, 5026338869833, 40210710958665, 321685687669321, 2573485501354569, 20587884010836553, 164703072086692425
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refs;
listen;
history;
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internal format)
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OFFSET
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0,3
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COMMENTS
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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
a(n) = A033138(3n-2). - Alexandre Wajnberg, May 31 2005
{1, 9, 73, 585, 4681, ...} is the binomial transform of A003950 . - Philippe DELEHAM, Jul 22 2005
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=8, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). [From Milan Janjic, Feb 21 2010]
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=9, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^n*charpoly(A,1). [From Milan Janjic, Feb 21 2010]
This is the sequence A(0,1;7,8;2) = A(0,1;8,0;1) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [From Wolfdieter Lang, Oct 18 2010]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Repunit.
W. Lang, Notes on certain inhomogeneous three term recurrences. [From Wolfdieter Lang, Oct 18 2010]
Index entries for sequences related to linear recurrences with constant coefficients, signature (9,-8).
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FORMULA
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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
a(0)=0, a(n)=8*a(n-1)+1 for n>0 . G.f.:x/((1-8x)*(1-x)) - Philippe DELEHAM, Oct 12 2006
Contribution from Wolfdieter Lang, Oct 18 2010: (Start)
a(n) = 7*a(n-1) + 8*a(n-2) + 2, a(0)=0, a(1)=1.
a(n) = 8*a(n-1) + a(n-2) - 8*a(n-3) = 9*a(n-1) - 8*a(n-2), a(0)=0, a(1)=1, a(2)=9. Observation by G. Detlefs. See the W.Lang comment and link. (End)
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EXAMPLE
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Octal.............decimal (comment from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 14 2007):
0....................0
1....................1
11...................9
111.................73
1111...............585
11111.............4681
111111...........37449
1111111.........299593
11111111.......2396745
111111111.....19173961
1111111111...153391689
etc. ...............etc.
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MAPLE
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a:=n->sum(8^(n-j), j=1..n): seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007
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MATHEMATICA
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Table[(8^n-1)/7, {n, 0, m}]
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PROG
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(Sage) [lucas_number1(n, 9, 8) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
(Sage) [gaussian_binomial(n, 1, 8) for n in xrange(0, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
(MAGMA) [(8^n-1)/7: n in [0..20]]; // Vincenzo Librandi, Sep 17 2011
(Maxima) A023001(n):=floor((8^n-1)/7)$
makelist(A023001(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
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CROSSREFS
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Cf. A007556.
Sequence in context: A126641 A081627 A164588 * A015454 A121246 A086226
Adjacent sequences: A022998 A022999 A023000 * A023002 A023003 A023004
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KEYWORD
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easy,nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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