OFFSET
0,2
COMMENTS
Coordination sequence for infinite tree with valency 11.
a(n) is sequence A003945(n-1) written in base 2: a(0)=1, a(n) for n >= 1: 2 times 1, (n-1) times 0. a(n) is also A007283(n-1) and A042950(n) for n >= 1 written in base 2. a(n) is also A098011(n+3) and A101229(n+10) for n >= 1 written in base 2. a(n) is also abs(A110164(n+1)) for n >= 1 written in base 2. - Jaroslav Krizek, Aug 17 2009
a(n) equals the numbers of words of length n on alphabet {0,1,...,10} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 [Corrected by David Nacin, Jun 02 2017]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 312
Index entries for linear recurrences with constant coefficients, signature (10).
FORMULA
a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 9. - Philippe Deléham, Jul 10 2005
G.f.: (1+x)/(1-10*x). - Paul Barry, Mar 22 2006
a(0) = 1, a(n) = 10^n + 10^(n-1) = 11*10^(n-1) for n >= 1. - Jaroslav Krizek, Aug 17 2009
E.g.f.: (11*exp(10*x) - 1)/10. - G. C. Greubel, Sep 24 2019
MAPLE
k:=11; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019
MATHEMATICA
Join[{1}, 11*10^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
PROG
(PARI) a(n)=11*10^n\10 \\ Charles R Greathouse IV, Aug 14 2015
(Magma) k:=11; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019
(Sage) k=11; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019
(GAP) k:=11;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Dec 04 2009
STATUS
approved