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A124696 Number of base 3 circular n-digit numbers with adjacent digits differing by 1 or less. 31
1, 3, 7, 15, 35, 83, 199, 479, 1155, 2787, 6727, 16239, 39203, 94643, 228487, 551615, 1331715, 3215043, 7761799, 18738639, 45239075, 109216787, 263672647, 636562079, 1536796803, 3710155683, 8957108167, 21624372015, 52205852195 (list; graph; refs; listen; history; text; internal format)
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, 3) 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 {1,2,3}. See theorem 3.3 in Knopfmacher and others. - Peter Luschny, Aug 13 2012

LINKS

Table of n, a(n) for n=0..28.

Arnold Knopfmacher, Toufik Mansour, Augustine Munagi, Helmut Prodinger, Smooth words and Chebyshev polynomials, arXiv:0809.0551v1 [math.CO], 2008.

FORMULA

Conjecture: a(n) = 1+(1-sqrt(2))^n+(1+sqrt(2))^n for n>0. a(n) = 3*a(n-1)-a(n-2)-a(n-3) for n>3. G.f.: -(2*x^3+x^2-1)/((x-1)*(x^2+2*x-1)). [Colin Barker, Nov 26 2012]

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

Sequence in context: A077970 A174284 A182892 * A081669 A086821 A007576

Adjacent sequences:  A124693 A124694 A124695 * A124697 A124698 A124699

KEYWORD

nonn,base

AUTHOR

R. H. Hardin, Dec 28 2006

STATUS

approved

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Last modified October 16 06:30 EDT 2019. Contains 328050 sequences. (Running on oeis4.)