A170734 Expansion of g.f.: (1+x)/(1-14*x).

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183360, 32669300067140567040, 457370200939967938560, 6403182813159551139840

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,...,14} with no two adjacent letters identical. -Milan Janjic, Jan 31 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..800
• 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 (14).

Crossrefs

Cf. A003945, A003954, A097805, A170733.

Programs

GAP

k:=15;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Magma

k:=15; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

Maple

k:=15; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 15*14^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
CoefficientList[Series[(1+x)/(1-14x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)

PARI

vector(26, n, k=15; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

Sage

k=15; [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)*15^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 15*14^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0) = 1, a(1) = 15, a(n) = 14*a(n-1). - Vincenzo Librandi, Dec 10 2012

E.g.f.: (15*exp(14*x) -1)/14. - G. C. Greubel, Sep 24 2019