A124707 Number of base 14 circular n-digit numbers with adjacent digits differing by 1 or less.

1, 14, 40, 92, 244, 644, 1750, 4802, 13324, 37244, 104770, 296222, 841114, 2396954, 6851920, 19639652, 56426044, 162453884, 468581890, 1353822062, 3917298334, 11350084334, 32926503100, 95626832432, 278010277474, 809008239794, 2356265478100, 6868253600552

Offset: 0

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base
• easy

Comments

[Empirical] a(base,n) = a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1

a(n) = T(n, 14) 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,..,14}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

• OEIS Wiki, Number of base k circular n-digit numbers with adjacent digits differing by d or less
• Index entries for linear recurrences with constant coefficients, signature (14,-78,208,-209,-198,627,-264,-441,358,100,-120,-5,10)

Crossrefs

Except for the first term, row 14 of A276562.

Cf. A002426, A124696.

Formula

G.f.: -(120*x^13 -55*x^12 -1200*x^11 +900*x^10 +2864*x^9 -3087*x^8 -1584*x^7 +3135*x^6 -792*x^5 -627*x^4 +416*x^3 -78*x^2 +1) / ((2*x-1) *(x^2-3*x+1) *(x^2+x-1) *(x^4+3*x^3-x^2-3*x+1) *(5*x^4-5*x^3-5*x^2+5*x-1)). - Alois P. Heinz, Apr 02 2025