A170733 Expansion of g.f.: (1+x)/(1-13*x).

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516518, 326173191714734, 4240251492291542, 55123269399790046, 716602502197270598, 9315832528564517774, 121105822871338731062, 1574375697327403503806

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Comments

For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,13} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, J. Int. Seq. 18 (2015) # 15.4.7.
• Index entries for linear recurrences with constant coefficients, signature (13).

Crossrefs

Cf. A003945, A003954, A170732.

Programs

GAP

k:=14;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Magma

k:=14; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

Maple

k:=14; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 14*13^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
CoefficientList[Series[(1+x)/(1-13x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
Join[{1},NestList[13#&,14,20]] (* Harvey P. Dale, Oct 09 2017 *)

PARI

vector(26, n, k=14; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

Sage

k=14; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*14^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 14*13^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0)=1, a(1)=14, a(n) = 13*a(n-1). - Vincenzo Librandi, Dec 10 2012

E.g.f.: (14*exp(13*x) - 1)/13. - G. C. Greubel, Sep 24 2019