This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208544 T(n,k) = Number of n-bead necklaces of k colors allowing reversal, with no adjacent beads having the same color. 8
 1, 2, 0, 3, 1, 0, 4, 3, 0, 0, 5, 6, 1, 1, 0, 6, 10, 4, 6, 0, 0, 7, 15, 10, 21, 3, 1, 0, 8, 21, 20, 55, 24, 13, 0, 0, 9, 28, 35, 120, 102, 92, 9, 1, 0, 10, 36, 56, 231, 312, 430, 156, 30, 0, 0, 11, 45, 84, 406, 777, 1505, 1170, 498, 29, 1, 0, 12, 55, 120, 666, 1680, 4291, 5580, 4435 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts .1.2..3...4....5.....6......7......8.......9......10......11.......12.......13 .0.1..3...6...10....15.....21.....28......36......45......55.......66.......78 .0.0..1...4...10....20.....35.....56......84.....120.....165......220......286 .0.1..6..21...55...120....231....406.....666....1035....1540.....2211.....3081 .0.0..3..24..102...312....777...1680....3276....5904....9999....16104....24882 .0.1.13..92..430..1505...4291..10528...23052...46185...86185...151756...254618 .0.0..9.156.1170..5580..19995..58824..149796..341640..714285..1391940..2559414 .0.1.30.498.4435.25395.107331.365260.1058058.2707245.6278140.13442286.26942565 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 264 terms from R. H. Hardin) FORMULA T(2n+1,k) = A208535(2n+1,k)/2 for n > 0, T(2n,k) = (A208535(2n,k) + (k*(k-1)^n)/2)/2. - Andrew Howroyd, Mar 12 2017 Empirical for row n: n=1: a(k) = k n=2: a(k) = (1/2)*k^2 - (1/2)*k n=3: a(k) = (1/6)*k^3 - (1/2)*k^2 + (1/3)*k n=4: a(k) = (1/8)*k^4 - (1/4)*k^3 + (3/8)*k^2 - (1/4)*k n=5: a(k) = (1/10)*k^5 - (1/2)*k^4 + k^3 - k^2 + (2/5)*k n=6: a(k) = (1/12)*k^6 - (1/2)*k^5 + (3/2)*k^4 - (7/3)*k^3 + (23/12)*k^2 - (2/3)*k n=7: a(k) = (1/14)*k^7 - (1/2)*k^6 + (3/2)*k^5 - (5/2)*k^4 + (5/2)*k^3 - (3/2)*k^2 + (3/7)*k EXAMPLE All solutions for n=7, k=3: ..1....1....1....1....1....1....1....1....1 ..2....2....2....2....2....2....2....2....2 ..3....3....1....1....3....1....3....1....3 ..1....1....2....2....1....2....2....3....2 ..2....3....3....3....3....1....3....1....3 ..3....1....1....2....2....2....2....2....1 ..2....3....3....3....3....3....3....3....3 MATHEMATICA T[n_, k_] := If[n == 1, k, (DivisorSum[n, EulerPhi[n/#]*(k-1)^#&]/n + If[ OddQ[n], 1-k, k*(k-1)^(n/2)/2])/2]; Table[T[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Oct 30 2017, after Andrew Howroyd *) PROG (PARI) T(n, k) = if(n==1, k, (sumdiv(n, d, eulerphi(n/d)*(k-1)^d)/n + if(n%2, 1-k, k*(k-1)^(n/2)/2))/2); for(n=1, 10, for(k=1, 10, print1(T(n, k), ", ")); print) \\ Andrew Howroyd, Oct 14 2017 CROSSREFS Cf. A081720, A208535, A106512. Main diagonal is A208538. Columns 3..7 are A208539, A208540, A208541, A208542, A208543. Row 2 is A000217(n-1). Row 3 is A000292(n-2). Row 4 is A002817(n-1). Row 5 is A164938(n-1). Row 6 is A027670(n-1). Sequence in context: A144257 A257232 A321980 * A208535 A284856 A276550 Adjacent sequences:  A208541 A208542 A208543 * A208545 A208546 A208547 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 27 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 06:01 EDT 2019. Contains 328291 sequences. (Running on oeis4.)