S000619


Number of ways to pair up {1^4, 2^4, ..., (2n)^4 } so the sum of each of the n pairs is prime.

1, 2, 2, 8, 12, 0, 12, 66, 150, 1374, 1860, 7076, 45352, 108230, 584842, 1583588, 7315594, 15166764, 129815288, 355293847, 3666243914, 16101936060, 106436359512, 444520484248, 2607800523879

1

S000619

It appears that s(6) is the only zero term. If eighth powers are used instead, then s(1) = 1 and then the terms up to s(35) are zero.

T. D. Noe, Plot of 25 terms

(Mma) Permanent[m_List] := With[{v = Array[x, Length[m]]}, Coefficient[Times @@ (m.v), Times @@ v]]; Table[m = Table[If[PrimeQ[(2*i)^4 + (2*j-1)^4], 1, 0], {i, n}, {j, n}]; Permanent[m], {n, 15}]

Cf. A000348.

nonn,hard,more

T. D. Noe, May 06 2015

© Tony D Noe 2014-2015