A336749 - OEIS

%I #18 Nov 07 2020 22:15:33

%S 1,0,1,1,1,3,2,3,6,5,10,12,14,25,27,40,57,68,104,133,177,255,324,454,

%T 617,811,1136,1507,2042,2803,3729,5109,6904,9290,12692,17070,23152,

%U 31430,42361,57567,77842,105279,142865,193040,261589,354316,479189,649498,878905

%N Number of circular arrangements of the first n positive integers such that adjacent terms have absolute difference 1 or 4.

%C Permutations in which adjacent terms sum to a particular value is a property central to the sequences A090460, A071984, A108658, A272259, and A107929.

%H Ethan P. White, Richard K. Guy, Renate Scheidler, <a href="https://arxiv.org/abs/2006.15250">Difference Necklaces</a>, arXiv:2006.15250 [math.CO], 2020. See Table A.1 p. 31.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,1,2,2,1,1,1).

%F a(n) = -a(n-1) + a(n-3) + a(n-4) + 2*a(n-5) + 2*a(n-6) + a(n-7) + a(n-8) + a(n-9) for n > 13.

%F G.f.: x^5*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)/(1 + x - x^3 - x^4 - 2*x^5 - 2*x^6 - x^7 - x^8 - x^9). - _Stefano Spezia_, Aug 03 2020

%t CoefficientList[ Series[(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)/(1 + x - x^3 - x^4 - 2*x^5 - 2*x^6 - x^7 - x^8 - x^9), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Nov 07 2020 *)

%Y See A079977 or A017899 for other sequences counting similar circular arrangements of positive integers.

%K nonn,easy

%O 5,6

%A _Ethan Patrick White_, Aug 02 2020