A003953 Expansion of g.f.: (1+x)/(1-10*x).

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000

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 to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (10).

Index entries for sequences related to trees

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

Cf. A003945, A003952.

Sequence in context: A167112 A167664 A167914 * A168688 A168736 A168784

Adjacent sequences: A003950 A003951 A003952 * A003954 A003955 A003956

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved