cp's OEIS Frontend

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

%I A124707 #21 Apr 30 2025 13:57:27
%S A124707 1,14,40,92,244,644,1750,4802,13324,37244,104770,296222,841114,
%T A124707 2396954,6851920,19639652,56426044,162453884,468581890,1353822062,
%U A124707 3917298334,11350084334,32926503100,95626832432,278010277474,809008239794,2356265478100,6868253600552
%N A124707 Number of base 14 circular n-digit numbers with adjacent digits differing by 1 or less.
%C A124707 [Empirical] a(base,n) = a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
%C A124707 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
%H A124707 OEIS Wiki, <a href="/wiki/Number_of_base_k_circular_n-digit_numbers_with_adjacent_digits_differing_by_d_or_less">Number of base k circular n-digit numbers with adjacent digits differing by d or less</a>
%H A124707 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (14,-78,208,-209,-198,627,-264,-441,358,100,-120,-5,10)
%F A124707 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
%o A124707 (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))
%Y A124707 Except for the first term, row 14 of A276562.
%Y A124707 Cf. A002426, A124696.
%K A124707 nonn,base,easy
%O A124707 0,2
%A A124707 _R. H. Hardin_, Dec 28 2006