A003951 Expansion of g.f.: (1+x)/(1-8*x).

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290624, 4947802324992, 39582418599936, 316659348799488, 2533274790395904, 20266198323167232, 162129586585337856, 1297036692682702848

Offset

0,2

Comments

Coordination sequence for infinite tree with valency 9.

Binomial transform is {1, 10, 91, 820, 7381, ...}, see A002452. - Philippe Deléham, Jul 22 2005

a(n) equals the 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]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 310

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (8).

Index entries for sequences related to trees

Formula

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

a(0) = 1; for n>0, a(n) = 9*8^(n-1). - Vincenzo Librandi, Nov 18 2010

a(0) = 1, a(1) = 9, a(n) = 8*a(n-1). - Vincenzo Librandi, Dec 10 2012

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

Maple

k:=9; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 9*8^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
CoefficientList[Series[(1+x)/(1-8*x), {x, 0, 25}], x] (* Vincenzo Librandi, Dec 10 2012 *)

Prog

(Magma) [1] cat [9*8^(n-1): n in [1..25]]; // Vincenzo Librandi, Dec 11 2012
(PARI) a(n)=if(n, 9*8^n/8, 1) \\ Charles R Greathouse IV, Mar 22 2016
(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.

Sequence in context: A170594 A170642 A170690 * A252702 A033135 A127053

Adjacent sequences: A003948 A003949 A003950 * A003952 A003953 A003954

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane, Dec 04 2009

Status

approved