This time, only 2nd order: (c44) (DONE,Z[N] := FACTOR(2*((Z[N-1]-2)*Z[N-1]^2*(Z[N-1]+1)-8*(Z[N-2]-2)*Z[N-2]^2*(Z[N-2]+1)^3*(2*Z[N-2]^2-2*Z[N-2]-1))/(Z[N-1]*(2*Z[N-1]+1)+(-2*Z[N-2]*(Z[N-2]+1)*(2*Z[N-2]+1)*(2*Z[N-2]+5))))); 2 (d44) z := factor(2 ((z - 2) z (z + 1) n n - 1 n - 1 n - 1 2 3 2 - 8 (z - 2) z (z + 1) (2 z - 2 z - 1)) n - 2 n - 2 n - 2 n - 2 n - 2 /(z (2 z + 1) + (- 2 z (z + 1) (2 z + 1) n - 1 n - 1 n - 2 n - 2 n - 2 (2 z + 5)))) n - 2 (c45) [Z[0] : (Y-1)*(2*Y+1),Z[1] : 2*(Y^2-1)*(4*Y^2-1)]; 2 2 (d45) [(y - 1) (2 y + 1), 2 (y - 1) (4 y - 1)] (c46) BLOCK([FANCY_DISPLAY : FALSE],FOR K FROM 0 THRU 5 DO PRINT(ARRAYMAKE(Z,[K]) = Z[K]))$ z = (y - 1) (2 y + 1) 0 2 2 z = 2 (y - 1) (4 y - 1) 1 2 2 z = 8 (y - 1) y (y + 1) (2 y - 1) (2 y + 1) (4 y - 3) 2 2 2 2 2 z = 32 (y - 1) y (y + 1) (2 y - 1) (2 y + 1) (2 y - 1) (4 y - 3) 3 4 2 (16 y - 16 y + 1) 2 2 2 2 z = 128 (y - 1) y (y + 1) (2 y - 1) (2 y + 1) (2 y - 1) (4 y - 3) 4 4 2 2 4 2 (8 y - 8 y + 1) (16 y - 16 y + 1) 8 6 4 2 (256 y - 512 y + 320 y - 64 y + 1) 2 2 2 2 z = 512 (y - 1) y (y + 1) (2 y - 1) (2 y + 1) (2 y - 1) (4 y - 3) 5 4 2 2 4 2 (8 y - 8 y + 1) (16 y - 16 y + 1) 8 6 4 2 2 (128 y - 256 y + 160 y - 32 y + 1) 8 6 4 2 (256 y - 512 y + 320 y - 64 y + 1) 16 14 12 10 8 (65536 y - 262144 y + 425984 y - 360448 y + 168960 y 6 4 2 - 43008 y + 5376 y - 256 y + 1) (c38) W[N] := FACTOR((W[N-1]*(W[N-1]^3+2*W[N-1]^2-6*W[N-1]-16)-W[N-2]*(W[N-2]+2)*(W[N-2]^6-2*W[N-2]^5-10*W[N-2]^4+8*W[N-2]^3+26*W[N-2]^2-4*W[N-2]-24))/(2*(W[N-1]^2+3*W[N-1]-W[N-2]*(W[N-2]+2)*(W[N-2]^2+6*W[N-2]+7)))); 3 2 (d38) w := factor((w (w + 2 w - 6 w - 16) n n - 1 n - 1 n - 1 n - 1 6 5 4 3 - w (w + 2) (w - 2 w - 10 w + 8 w n - 2 n - 2 n - 2 n - 2 n - 2 n - 2 2 2 + 26 w - 4 w - 24))/(2 (w + 3 w n - 2 n - 2 n - 1 n - 1 2 - w (w + 2) (w + 6 w + 7)))) n - 2 n - 2 n - 2 n - 2 (c39) [W[0] : 2*(2*X^2+X-1),W[1] : 4*X^2*(4*X^2-3)]; 2 2 2 (d39) [2 (2 x + x - 1), 4 x (4 x - 3)] (c40) FOR K FROM 0 THRU 5 DO PRINT(ARRAYMAKE(W,[K]) = W[K])$ 2 w = 2 (2 x + x - 1) 0 2 2 w = 4 x (4 x - 3) 1 2 2 4 2 w = 4 (2 x - 1) (16 x - 16 x + 1) 2 4 2 2 8 6 4 2 w = 4 (8 x - 8 x + 1) (256 x - 512 x + 320 x - 64 x + 1) 3 8 6 4 2 2 w = 4 (128 x - 256 x + 160 x - 32 x + 1) 4 16 14 12 10 8 (65536 x - 262144 x + 425984 x - 360448 x + 168960 x 6 4 2 - 43008 x + 5376 x - 256 x + 1) 16 14 12 10 w = 4 expt(32768 x - 131072 x + 212992 x - 180224 x 5 8 6 4 2 + 84480 x - 21504 x + 2688 x - 128 x + 1, 2) 32 30 28 (4294967296 x - 34359738368 x + 124554051584 x 26 24 22 - 270582939648 x + 392586854400 x - 401311006720 x 20 18 16 + 297124495360 x - 161296154624 x + 64266436608 x 14 12 10 8 - 18627952640 x + 3852599296 x - 550371328 x + 51597312 x 6 4 2 - 2924544 x + 87040 x - 1024 x + 1) --rwg