Entire Function that enumerates the lattice points

Entire Function that enumerates the lattice points
0 0 1 2 3 4 5 6 7 8
0 1 3 6 10 15 21 28 36 45
1 2 5 9 14 20 27 35 44 54
2 4 8 13 19 26 34 43 53 64
3 7 12 18 25 33 42 52 63 75
4 11 17 24 32 41 51 62 74 87
5 16 23 31 40 50 61 73 86 100
6 22 30 39 49 60 72 85 99 114
7 29 38 48 59 71 84 98 113 129
8 37 47 58 70 83 97 112 128 145


Reference: G. Polya and G. Szego, Problems and Theorems in Analysis, II, p. 151.