A003952 Expansion of g.f.: (1+x)/(1-9*x).

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690, 1500946352969991210, 13508517176729920890

Offset

0,2

Comments

Coordination sequence for infinite tree with valency 10.

The n-th term of the coordination sequence of the infinite tree with valency 2m is the same as the number of reduced words of size n in the free group on m generators. In the five sequences A003946, A003948, A003950, A003952, A003954 m is 2, 3, 4, 5, 6 . - Avi Peretz (njk(AT)netvision.net.il), Feb 23 2001 and Ola Veshta (olaveshta(AT)my-deja.com), Mar 30 2001

Except 1, all terms are in A033583. - Vincenzo Librandi, May 26 2014

For n>=1, a(n) equals the number of words of length n on alphabet {0,1,...,9} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 [Corrected by David Nacin, May 31 2017]

a(n) is the number of sequences over the alphabet {0,1,...,9} of length n such that no two consecutive terms have distance 5. - David Nacin, May 31 2017

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 311

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (9).

Index entries for sequences related to trees

Formula

a(n) = (10*9^n - 0^n)/9. Binomial transform is A000042. - Paul Barry, Jan 29 2004

G.f.: (1+x)/(1-9*x). - Philippe Deléham, Jan 31 2004

a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 8. - Philippe Deléham, Jul 10 2005

The Hankel transform of this sequence is: [1,-10,0,0,0,0,0,0,0,...]. - Philippe Deléham, Nov 21 2007

E.g.f.: (10*exp(9*x) - 1)/9. - G. C. Greubel, Sep 24 2019

Maple

k:= 10; seq(`if`(n = 0, 1, k*(k-1)^(n-1)), n = 0..20); # modified by G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 10*9^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
Join[{1}, NestList[9#&, 10, 20]] (* Harvey P. Dale, Sep 01 2021 *)

Prog

(Magma) [(10*9^n-0^n)/9: n in [0..20] ]; // Vincenzo Librandi, Aug 19 2011
(PARI) a(n)=10*9^n\9 \\ Charles R Greathouse IV, Sep 08 2011
(Sage) k=10; [1]+[k*(k-1)^(n-1) for n in (1..20)] # G. C. Greubel, Sep 24 2019
(GAP) k:=10;; Concatenation([1], List([1..20], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Crossrefs

Cf. A003949, A003950, A003951.

Sequence in context: A170595 A170643 A170691 * A252703 A033136 A061206

Adjacent sequences: A003949 A003950 A003951 * A003953 A003954 A003955

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 15 1996

Extensions

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

Status

approved