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 A283614 T(n,k) = number of circular arrays of n 1's, n -1's, and k 0's such that no two adjacent elements are equal. 1
 1, 2, 6, 4, 2, 10, 24, 28, 12, 2, 14, 56, 132, 180, 132, 40, 2, 18, 100, 352, 804, 1196, 1120, 600, 140, 2, 22, 156, 728, 2324, 5196, 8160, 8840, 6300, 2660, 504, 2, 26, 224, 1300, 5320, 15844, 34872, 56848, 67900, 57820, 33264, 11592, 1848, 2, 30, 304, 2108, 10512, 39064, 110480, 240288, 402556, 515844, 496944, 348600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The array is circular in the sense that the first and last elements are adjacent. For linear arrays see A283613. LINKS FORMULA G.f.: 2*(x*y+1)/sqrt((1-y)*(1-(2*x+1)^2*y))-1. T(n,0)  G.f.: (1+y)/(1-y). T(n,1)  G.f.: 2*y*(3-y)/(1-y)^2. T(n,2)  G.f.: 4*y*(1+3*y-y^2)/(1-y)^3. T(n,3)  G.f.: 4*y^2*(1+y)*(7-2*y)/(1-y)^4. T(n,4)  G.f.: 4*y^2*(3+30*y+6*y^2-4*y^3)/(1-y)^5. T(n,5)  G.f.: 4*y^3*(33+101*y-8*y^3)/(1-y)^6. T(n,n) = A110707(n). T(n,2*n) = 2*binomial(2*n,n). Sum_{2*n+k = m} T(n,k) = A265118(m), m > 3. EXAMPLE The table starts with columns k=0..10 and rows n=0..5:   | 0  1   2   3    4    5    6    7    8    9  10 ----------------------------------------------------------------- 0 | 1 1 | 2  6   4 2 | 2 10  24  28   12 3 | 2 14  56 132  180  132   40 4 | 2 18 100 352  804 1196 1120  600  140 5 | 2 22 156 728 2324 5196 8160 8840 6300 2660 504 For n=2, k=3, the 28 arrays are: [+0-0+0-] [+0+0-0-] [0-+0+0-] [0-0+0+-] [0+-0+0-] [0+0-+0-] [0+0-0+-] [0+0+-0-] [-0-0+0+] [-0+0-0+] [0-+0-0+] [0-0-+0+] [0-0+-0+] [0-0+0-+] [0+-0-0+] [0+0-0-+] [-+0-0+0] [-+0+0-0] [-0-+0+0] [-0+-0+0] [-0+0-+0] [-0+0+-0] [+-0-0+0] [+-0+0-0] [+0-+0-0] [+0-0-+0] [+0-0+-0] [+0+-0-0] MATHEMATICA nmax=8; Flatten[CoefficientList[Series[CoefficientList[Series[2*(x*y + 1)/Sqrt[(1 - y)*(1 - (2*x + 1)^2*y)] - 1, {y, 0, nmax }], y], {x, 0, 2nmax + 1 }], x]] (* Indranil Ghosh, Apr 02 2017 *) CROSSREFS Cf. A110707, A265118, A283613. Sequence in context: A074382 A061350 A046276 * A003571 A068457 A299402 Adjacent sequences:  A283611 A283612 A283613 * A283615 A283616 A283617 KEYWORD nonn,tabf AUTHOR Stefan Hollos, Apr 01 2017 STATUS approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)