+ )n ! (1 − )n |- ! 0 | 1 + 0 = 1 | 1 − 0 = 1 |- ! 1 | 1 + 1 = 2.41421… | 1 − 1 = −0.41421… |- ! 2 | 3 + 2 = 5.82842… | 3 − 2 = 0.17157… |- ! 3 | 7 + 5 = 14.07106… | 7 − 5 = −0.07106… |- ! 4 | 17 + 12 = 33.97056… | 17 − 12 = 0.02943… |- ! 5 | 41 + 29 = 82.01219… | 41 − 29 = −0.01219… |- ! 6 | 99 + 70 = 197.9949… | 99 − 70 = 0.0050… |- ! 7 | 239 + 169 = 478.00209… | 239 − 169 = −0.00209… |- ! 8 | 577 + 408 = 1153.99913… | 577 − 408 = 0.00086… |- ! 9 | 1393 + 985 = 2786.00035… | 1393 − 985 = −0.00035… |- ! 10 | 3363 + 2378 = 6725.99985… | 3363 − 2378 = 0.00014… |- ! 11 | 8119 + 5741 = 16238.00006… | 8119 − 5741 = −0.00006… |- ! 12 | 19601 + 13860 = 39201.99997… | 19601 − 13860 = 0.00002… |} The coefficients are the half-companion Pell numbers Hn and the Pell numbers Pn which are the (non-negative) solutions to . A square triangular number is a number which is both the t-th triangular number and the s-th square number. A near-isosceles Pythagorean triple is an integer solution to where . The next table shows that splitting the odd number Hn into nearly equal halves gives a square triangular number when n is even and a near isosceles Pythagorean triple when n is odd. All solutions arise in this manner. {| class="wikitable" style="text-align:center" |- !n !Hn !Pn !t !t + 1 !s !a !b !c |- !0 |1 |0 |0 |1 |0 |style="background: grey;"| |style="background: grey;"| |style="background: grey;"| |- !1 |1 |1 |style="background: grey;"| |style="background: grey;"| |style="background: grey;"| |0 |1 |1 |- !2 |3 |2 |1 |2 |1 |style="background: grey;"| |style="background: grey;"| |style="background: grey;"| |- !3 |7 |5 |style="background: grey;"| |style="background: grey;"| |style="background: grey;"| |3 |4 |5 |- !4 |17 |12 |8 |9 |6 |style="background: grey;"| |style="background: grey;"| |style="background: grey;"| |- !5 |41 |29 |style="background: grey;"| |style="background: grey;"| |style="background: grey;"| |20 |21 |29 |- !6 |99 |70 |49 |50 |35 |style="background: grey;"| |style="background: grey;"| |style="background: grey;"| |- !7 |239