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%I #10 Sep 08 2019 03:14:14
%S 1,1,1,1,1,1,1,1,2,4,4,8,6,14,14,44,22,30,12,41,137,667,401,517,149,
%T 286,306,1312,1940,23546,23886,23886,68285,728501,241424,555302,
%U 630441,4175810,7996830,87591010,101316606,148078428,92744140,298180464,241949668,1090944470
%N Number of ways of pairing the even squares of the numbers 1 to n with the odd squares of the numbers n+1 to 2n such that each pair sums to a prime. a(1) is defined to be 1.
%C It appears that a pairing is always possible. The Mathematica program uses backtracking to find all solutions. The Print statement can be uncommented to print all solutions. The product of this sequence and A077763 gives A077762.
%H Bert Dobbelaere, <a href="/A077764/b077764.txt">Table of n, a(n) for n = 1..50</a>
%e a(5)=1 because only one pairing is possible: 4+49=53, 16+81=97.
%t try[lev_] := Module[{j}, If[lev>n, (*Print[soln]; *) cnt++, For[j=1, j<=Length[s[[lev]]], j++, If[ !MemberQ[soln, s[[lev]][[j]]], soln[[lev]]=s[[lev]][[j]]; try[lev+2]; soln[[lev]]=0]]]]; maxN=28; For[lst2={1}; n=2, n<=maxN, n++, s=Table[{}, {n}]; For[i=2, i<=n, i=i+2, For[j=n+1, j<=2n, j++, If[PrimeQ[i^2+j^2], AppendTo[s[[i]], j]]]]; soln=Table[0, {n}]; cnt=0; try[2]; AppendTo[lst2, cnt]]; lst2
%Y Cf. A077762, A077763.
%K nonn
%O 1,9
%A _T. D. Noe_, Nov 15 2002
%E a(29)-a(46) from _Bert Dobbelaere_, Sep 08 2019
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