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

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A252897 Rainbow Squares: a(n) = number of ways to pair the integers 1 to 2n so that the sum of each pair is a square. 4
 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 6, 18, 12, 36, 156, 295, 429, 755, 2603, 7122, 19232, 32818, 54363, 172374, 384053, 933748, 1639656, 4366714, 20557751, 83801506, 188552665, 399677820, 640628927, 2175071240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,14 COMMENTS The original sequence is from Henri Picciotto who asked for which n is such a pairing possible: A253472. The name "rainbow squares" refers to the use of this problem in the elementary school classroom where children draw colored connecting "rainbows" to make the pairings. Number of perfect matchings in the graph with vertices 1 to 2n and edges {i,j} where i+j is a square. - Robert Israel, Mar 22 2015 LINKS Gordon Hamilton, Kiran S. Kedlaya, and Henri Picciotto, Square-Sum Pair Partitions, The College Mathematics Journal, Vol. 46, No. 4 (September 2015), pp. 264-269. EXAMPLE One of the solutions for n=13 consists of the following pairings of 1-26: {1,15}, adding to 16; {2,23}, {3,22}, {4,21}, {5,20}, {6,19}, {7,18}, {8,17}, {9,16}, {11,14}, {12, 13}, each adding to 25; {10,26}, adding to 36; {24,25}, adding to 49. There are five other such pairings possible, so a(13) = 6. MAPLE F:= proc(S)   option remember;   local s, ts;   if nops(S) = 0 then return 1 fi;   s:= S[-1];   ts:= select(t -> issqr(s+t), S minus {s});   add(procname(S minus {s, t}), t = ts); end proc: seq(F({\$1..2*n}), n = 0 .. 24); # Robert Israel, Mar 22 2015 MATHEMATICA F[S_] := F[S] = Module[{s, ts}, If[Length[S] == 0, Return[1]]; s = S[[-1]]; ts = Select[S ~Complement~ {s}, IntegerQ[Sqrt[s + #]]&]; Sum[F[S ~Complement~ {s, t}], {t, ts}]]; Table[Print[n]; F[Range[2 n]], {n, 0, 24}] (* Jean-François Alcover, Mar 19 2019, after Robert Israel *) CROSSREFS Cf. A253472, A278329, A278339. Sequence in context: A274877 A091014 A097370 * A174904 A074390 A255617 Adjacent sequences:  A252894 A252895 A252896 * A252898 A252899 A252900 KEYWORD nonn,more AUTHOR Gordon Hamilton, Mar 22 2015 EXTENSIONS a(26)-a(30) from Hiroaki Yamanouchi, Mar 25 2015 a(31) from Alois P. Heinz, Nov 16 2016 a(32)-a(36) from Linus and Joost VandeVondele, Jun 07 2018 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 November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)