A336749 - OEIS

A336749

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

1, 0, 1, 1, 1, 3, 2, 3, 6, 5, 10, 12, 14, 25, 27, 40, 57, 68, 104, 133, 177, 255, 324, 454, 617, 811, 1136, 1507, 2042, 2803, 3729, 5109, 6904, 9290, 12692, 17070, 23152, 31430, 42361, 57567, 77842, 105279, 142865, 193040, 261589, 354316, 479189, 649498, 878905

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OFFSET

5,6

COMMENTS

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

LINKS

Table of n, a(n) for n=5..53.

Ethan P. White, Richard K. Guy, Renate Scheidler, Difference Necklaces, arXiv:2006.15250 [math.CO], 2020. See Table A.1 p. 31.

Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1,2,2,1,1,1).

FORMULA

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.

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

MATHEMATICA

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 *)

CROSSREFS

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

Sequence in context: A058691 A281667 A368102 * A214297 A022472 A014679

Adjacent sequences: A336746 A336747 A336748 * A336750 A336751 A336752

KEYWORD

nonn,easy

AUTHOR

Ethan Patrick White, Aug 02 2020

STATUS

approved