Number of ways that n can be written as the sum of two positive nondecreasing squares and a prime.
0, 0, 0, 1, 1, 0, 2, 1, 1, 2, 1, 2, 3, 0, 4, 2, 1, 2, 3, 3, 4, 3, 3, 3, 4, 1, 4, 4, 3, 3, 6, 3, 4, 4, 2, 6, 6, 1, 8, 3, 3, 6, 6, 4, 6, 4, 5, 7, 6, 3, 6, 6, 5, 6, 9, 5, 8, 6, 3, 7, 8, 2, 12, 6, 4, 7, 7, 6, 10, 7, 7, 9, 7, 5, 9, 9, 7, 9, 10, 4, 12, 7, 5, 12, 9, 4
1
T. D. Noe, Plot of 10000 terms
T. D. Noe, Table of 10000 terms
(Mma) nn = 10; s = Select[Sort[Flatten[Table[x^2 + y^2 + p, {x, nn}, {y, x, nn}, {p, Prime[Range[PrimePi[nn^2]]]}]]], # <= nn^2 &]; t = Table[0, {nn^2}]; s = Tally[s]; Do[t[[i[[1]]]] = i[[2]], {i, s}]; t
Cf. S000125-S000136 (2 to 4 squares), A002471, A064272 (1 square).
nonn
T. D. Noe, Jul 11 2014