A003954 Expansion of g.f.: (1+x)/(1-11*x).

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812, 551396758362865932, 6065364341991525252, 66719007761906777772, 733909085380974555492

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Coordination sequence for infinite tree with valency 12.

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.

For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,11} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 313.
• Index to divisibility sequences.
• Index entries for linear recurrences with constant coefficients, signature (11).
• Index entries for sequences related to trees.

Crossrefs

Cf. A003946, A003948, A003950, A003952, A003953, A003954, A029653.

Programs

GAP

Concatenation([1], List([1..20], n-> 12*11^(n-1) )); # G. C. Greubel, Sep 23 2019

Magma

[1] cat [12*11^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012

Maple

k:=12; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 12*11^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
CoefficientList[Series[(1+x)/(1-11x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)

PARI

a(n)=12*11^n\11 \\ Charles R Greathouse IV, Aug 14 2015

Sage

[1]+[12*11^(n-1) for n in (1..20)] # G. C. Greubel, Sep 23 2019

Formula

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

G.f.: (1+x)/(1-11*x). The Hankel transform of this sequence is [1,-12,0,0,0,0,0,0,0,...]. - Philippe Deléham, Nov 21 2007

a(0) = 1; for n>0, a(n) = 12*11^(n-1). - Vincenzo Librandi, Nov 18 2010

a(0) = 1, a(1)=12, a(n) = 11*a(n-1). - Vincenzo Librandi, Dec 10 2012

E.g.f.: (12*exp(11*x) - 1)/11. - Elmo R. Oliveira, Mar 24 2025

Extensions

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