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A003954 Expansion of g.f.: (1+x)/(1-11*x). 57
1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

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

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 *)

PROG

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

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

CROSSREFS

Cf. A003952, A003953.

Sequence in context: A167113 A167665 A167916 * A168689 A168737 A168785

Adjacent sequences:  A003951 A003952 A003953 * A003955 A003956 A003957

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)