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 A208600 Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero. 2
 26, 297, 1564, 5457, 14838, 34153, 69784, 130401, 227314, 374825, 590580, 895921, 1316238, 1881321, 2625712, 3589057, 4816458, 6358825, 8273228, 10623249, 13479334, 16919145, 21027912, 25898785, 31633186, 38341161, 46141732, 55163249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 6 of A208597. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = (44/15)*n^5 + (22/3)*n^4 + (23/3)*n^3 + (14/3)*n^2 + (12/5)*n + 1. Conjectures from Colin Barker, Mar 07 2018: (Start) G.f.: x*(26 + 141*x + 172*x^2 + 8*x^3 + 6*x^4 - x^5) / (1 - x)^6. a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6. (End) EXAMPLE Some solutions for n=4: -4 -4 -4 -3 -4 -2 -4 -4 -4 -4 -3 -4 -4 -3 -3 -1 4 3 2 2 -3 -2 -1 2 0 -1 3 4 2 -1 3 0 0 2 -1 3 -2 2 0 -3 4 2 -3 -2 1 2 0 -1 1 1 -3 0 3 0 -1 0 -1 1 3 0 3 -2 -2 0 -1 1 3 0 4 -2 4 3 4 4 -3 1 -2 4 0 -1 0 -3 3 -2 2 4 2 2 -3 -2 3 1 0 0 2 3 CROSSREFS Sequence in context: A020925 A224331 A125414 * A010831 A022718 A014472 Adjacent sequences: A208597 A208598 A208599 * A208601 A208602 A208603 KEYWORD nonn AUTHOR R. H. Hardin, Feb 29 2012 STATUS approved

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Last modified April 22 21:44 EDT 2024. Contains 371906 sequences. (Running on oeis4.)