The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A003951

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A003951

Expansion of g.f.: (1+x)/(1-8*x).
(history; published version)

#59 by Charles R Greathouse IV at Thu Sep 08 08:44:32 EDT 2022

PROG

(MAGMAMagma) [1] cat [9*8^(n-1): n in [1..25]]; // Vincenzo Librandi, Dec 11 2012

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#58 by Sean A. Irvine at Tue Sep 24 21:05:23 EDT 2019

STATUS

proposed

approved

#57 by G. C. Greubel at Tue Sep 24 17:13:24 EDT 2019

STATUS

editing

proposed

#56 by G. C. Greubel at Tue Sep 24 17:12:23 EDT 2019

NAME

GExpansion of g.f.: (1+x)/(1-8*x).

FORMULA

a(n) = Sum_{ 0<=k<=0..n } A029653(n, k)*x^k for x = 7. - Philippe Deléham, Jul 10 2005

E.g.f.: (9*exp(8*x) -1)/8. - G. C. Greubel, Sep 24 2019

MAPLE

k := 9; seq(`if `(n = 0 then , 1 else , k*(k-1)^(n-1); fi), n = 0..25); # modified by _G. C. Greubel_, Sep 24 2019

MATHEMATICA

q = 9; Join[{a = 1}, Table[If[n != 0, a = q*a - a, a = q*a], {n, 0, 25}]] (* and *) Join[{1}, 9*8^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)

CoefficientList[Series[(1 + x)/(1 - 8*x), {x, 0, 4025}], x] (* Vincenzo Librandi, Dec 10 2012 *)

PROG

(MAGMA) [1] cat [9*8^(n-1): n in [1..2025]]; // Vincenzo Librandi, Dec 11 2012

(Sage) k=9; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

(GAP) k:=9;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

CROSSREFS

Cf. A003945.

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#55 by N. J. A. Sloane at Wed May 31 22:33:45 EDT 2017

STATUS

proposed

approved

#54 by Alois P. Heinz at Wed May 31 19:32:17 EDT 2017

STATUS

editing

proposed

Discussion

Wed May 31

19:37

David Nacin: I agree.  I've been using that convention for the sequences I've added, but didn't know if it was proper to change someone else's to that as well.

#53 by Alois P. Heinz at Wed May 31 19:31:27 EDT 2017

COMMENTS

For n>=1, a(n) equals the numbers number of words of length n on alphabet {0,1,...,8} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 [Corrected by David Nacin, May 31 2017]

STATUS

proposed

editing

Discussion

Wed May 31

19:32

Alois P. Heinz: it is true for all n>=0.  For n=0 we have the empty word.

#52 by David Nacin at Wed May 31 14:18:36 EDT 2017

STATUS

editing

proposed

#51 by David Nacin at Wed May 31 14:18:30 EDT 2017

COMMENTS

For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,8} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 [Corrected by _David Nacin_, May 31 2017]

STATUS

approved

editing

#50 by N. J. A. Sloane at Tue Apr 18 07:02:50 EDT 2017

LINKS

INRIA Algorithms Project, <a href="http://algoecs.inria.fr/ecsservices/ecsstructure?searchType=1&service=Search&searchTermsnbr=310">Encyclopedia of Combinatorial Structures 310</a>

Discussion

Tue Apr 18

07:02

OEIS Server: https://oeis.org/edit/global/2632