A170732 Expansion of g.f.: (1+x)/(1 - 12*x).

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622784, 2403495365635473408, 28841944387625680896, 346103332651508170752

Offset: 0

Author

N. J. A. Sloane, Dec 05 2009

Keywords

• nonn
• easy

Comments

For n >= 1, a(n) equals the number of words of length n-1 on the alphabet {0,1,...,12} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015

Links

• Kenny Lau, Table of n, a(n) for n = 0..926
• 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 (12).

Crossrefs

Cf. A003945, A003953, A003954.

Programs

GAP

k:=13;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Magma

k:=13; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

Maple

k:=13; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 13*12^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
Join[{1},NestList[12#&,13,20]] (* Harvey P. Dale, Nov 24 2024 *)

PARI

a(n)=if(n,13*12^(n-1),1) \\ Charles R Greathouse IV, Jul 01 2016

Python

for i in range(1001):print(i,13*12**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

Sage

k=13; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

Formula

a(0)=1; for n > 0, a(n) = 13*12^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (13*exp(12*x) - 1)/12. - G. C. Greubel, Sep 24 2019