OFFSET
0,2
COMMENTS
[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 11) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,11}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012
FORMULA
G.f.: (1 - 45*x^2 + 150*x^3 - 18*x^4 - 504*x^5 + 490*x^6 + 300*x^7 - 420*x^8 - 32*x^9 + 72*x^10) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x + 2*x^2 + 4*x^3 - 2*x^4)) (conjectured). - Colin Barker, Jun 03 2017
PROG
(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>1)+($[(i+1)mod N]`-$[i]`>1))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
R. H. Hardin, Dec 28 2006
STATUS
approved