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 A208826 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero. 1
 7, 45, 155, 415, 905, 1755, 3085, 5077, 7891, 11761, 16887, 23555, 32005, 42575, 55545, 71305, 90175, 112597, 138931, 169671, 205217, 246115, 292805, 345885, 405835, 473305, 548815, 633067, 726621, 830231, 944497, 1070225, 1208055 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 5 of A208825. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7). Conjectures from Colin Barker, Jul 06 2018: (Start) G.f.: x*(7 + 24*x + 27*x^2 + 30*x^3 + 5*x^4 - 2*x^5 + x^6) / ((1 - x)^5*(1 + x)^2). a(n) = (23*n^4 + 46*n^3 + 58*n^2 + 44*n + 24) / 24 for n even. a(n) = (23*n^4 + 46*n^3 + 58*n^2 + 26*n + 15) / 24 for n odd. (End) EXAMPLE Some solutions for n=3: -2 -2 -2 -2 -3 -3 -2 -2 -2 -2 -1 0 -3 -1 -2 -1 -2 0 -1 -1 -2 -2 1 0 -1 1 -1 0 -2 0 0 0 1 1 -1 -2 2 0 0 -2 1 -1 -1 0 3 0 0 0 0 1 3 2 2 3 0 1 1 1 1 0 1 -1 -1 1 3 0 1 3 1 2 1 3 1 1 2 0 1 2 3 0 CROSSREFS Cf. A208825. Sequence in context: A153492 A107125 A212105 * A206808 A197369 A059937 Adjacent sequences: A208823 A208824 A208825 * A208827 A208828 A208829 KEYWORD nonn AUTHOR R. H. Hardin, Mar 01 2012 STATUS approved

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Last modified June 5 01:39 EDT 2023. Contains 363130 sequences. (Running on oeis4.)