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 A072506 Triangle giving T(n,m) = number of necklaces of two colors with 2n beads of which m=1..n are black. 2
 1, 1, 2, 1, 3, 4, 1, 4, 7, 10, 1, 5, 12, 22, 26, 1, 6, 19, 43, 66, 80, 1, 7, 26, 73, 143, 217, 246, 1, 8, 35, 116, 273, 504, 715, 810, 1, 9, 46, 172, 476, 1038, 1768, 2438, 2704, 1, 10, 57, 245, 776, 1944, 3876, 6310, 8398, 9252, 1, 11, 70, 335, 1197, 3399, 7752 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Left half of even rows of triangle A047996 (with the leftmost edge discarded). LINKS Table of n, a(n) for n=1..62. FORMULA (1/(2n)) Sum_{d |(2n, m)} phi(d)*binomial(2n/d, m/d) MATHEMATICA Table[(Plus@@(EulerPhi[ # ]Binomial[2n/#, m/# ] &)/@Intersection[Divisors[2n], Divisors[m]])/(2n), {n, 13}, {m, n}] CROSSREFS Penultimate entries give binary necklaces of n-1 black beads and n+1 white beads, presumably A007595, antepenultimate entries give binary necklaces of n-2 black beads and n+2 white beads, presumably A003444. Cf. A047996, A003444. Sequence in context: A076832 A078925 A361042 * A188236 A181851 A210231 Adjacent sequences: A072503 A072504 A072505 * A072507 A072508 A072509 KEYWORD nonn,tabl AUTHOR Wouter Meeussen, Aug 03 2002 STATUS approved

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Last modified April 21 19:32 EDT 2024. Contains 371885 sequences. (Running on oeis4.)