The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108658 Number of the essentially different permutations of the numbers 0 to n such that the sum of adjacent numbers is a square. 3
 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 4, 4, 0, 0, 4, 5, 2, 8, 7, 47, 72, 135, 283, 158, 164, 1948, 1467, 2998, 20561, 66700, 130236, 153058, 181635, 239386, 343189, 1600832, 5001577, 16859525, 45119463, 66785667, 218923884, 393626778, 665307164, 3111228585, 2156371427 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,16 COMMENTS A108658 Square chains (reversals not counted and circles counted once). There is no solution for n=2-13,18-19 (note offset=0). For n=0 and n=1 we have trivial square circles (which are also known as square loops). Square circles seem to appear for all n>30, see A108661. Cf. A090460 for 1-to-n case. LINKS EXAMPLE n=14: one solution {8,1,0,9,7,2,14,11,5,4,12,13,3,6,10}; n=15: three solutions {0,9,7,2,14,11,5,4,12,13,3,6,10,15,1,8}, {5,11,14,2,7,9,0,4,12,13,3,6,10,15,1,8}, {8,1,0,9,7,2,14,11,5,4,12,13,3,6,10,15}; n=16: four solutions {0,16,9,7,2,14,11,5,4,12,13,3,6,10,15,1,8}, {5,11,14,2,7,9,16,0,4,12,13,3,6,10,15,1,8}, {8,1,0,16,9,7,2,14,11,5,4,12,13,3,6,10,15}, {8,1,15,10,6,3,13,12,4,5,11,14,2,7,9,0,16}; etc. MATHEMATICA SquareQ[n_]:=IntegerQ[Sqrt[n]]; try[lev_]:=Module[{t, j, circular}, If[lev>n+1, circular=SquareQ[soln[[1]]+soln[[n+1]]]; If[(!circular&&soln[[1]]

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 June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)