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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 406 "f := proc(n) ;\n#ru
ns a recurrence for 1 by n rectangles forwards and back with weights o
n #edges and vertices.\nif n = 4 then a(1)*a(2)*a(3)*a(4) + x(1)*a(3)*
a(4) + a(1)*x(2)*a(4) + a(1)*a(2)*x(3) + x(1)*x(3)\nelif n = 3 then a(
1)*a(2)*a(3) + x(1)*a(3) + a(1)*x(2)\nelif n = 2 then a(1)*a(2) + x(1)
\nelif n > 4 then simplify(a(n)*f(n-1) + x(n-1)*f(n-2))\nelse simplify
((f(n+2) - a(n+2)*f(n+1))/x(n+1) )\nfi;\nend;" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%\"fGR6#%\"nG6\"F(F(@+/9$\"\"%,,**-%\"aG6#\"\"\"F2-F06
#\"\"#F2-F06#\"\"$F2-F06#F,F2F2*(-%\"xGF1F2F6\"\"\"F9F>F2*(F/F>-F=F4F2
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" 
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 " 0 "" {MPLTEXT 1 0 888 "F := proc(n);\n#runs 2 by n forwards and bac
kwards with weights on vertices and edges\nG := proc(n);\nif n = 1 the
n b(1)\nelif n = 2 then b(2)*F(1) + a(1)*z(1)\nelif n > 2 then simplif
y(b(n)*F(n-1) +z(n-1)*H(n-1))\nelse simplify( (G(n+2) - b(n+2)*F(n+1) \+
- z(n+1)*a(n+1)*F(n))/(z(n+1)*x(n)) )\nfi;\nend;\n\nH := proc(n);\nif \+
n = 1 then a(1)\nelif n = 2 then a(2)*F(1) + b(1)*x(1)\nelif n > 2 the
n simplify( a(n)*F(n-1) + x(n-1)*G(n-1) )\nelse simplify( (H(n+2) - a(
n+2)*F(n+1) - x(n+1)*b(n+1)*F(n))/(x(n+1)*z(n)) )\nfi;\nend;\n\nif n =
 1 then a(1)*b(1) + y(1)\nelif n = 2 then simplify( (a(2)*b(2) + y(2))
*F(1) + x(1)*b(1)*b(2) + a(1)*a(2)*z(1) + x(1)*z(1) )\nelif n > 2 then
 simplify( (a(n)*b(n) + y(n))*F(n-1) + b(n)*x(n-1)*G(n-1) + a(n)*z(n-1
)*H(n-1) + x(n-1)*z(n-1)*F(n-2) )\nelse simplify( (F(n+2) - (a(n+2)*b(
n+2) + y(n+2))*F(n+1) - b(n+2)*x(n+1)*G(n+1) - a(n+2)*z(n+1)*H(n+1))/(
x(n+1)*z(n+1)) )\nfi;\nend;" }}{PARA 7 "" 1 "" {TEXT -1 41 "Warning, `
G` is implicitly declared local" }}{PARA 7 "" 1 "" {TEXT -1 41 "Warnin
g, `H` is implicitly declared local" }}{PARA 12 "" 1 "" {XPPMATH 20 "6
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F(3);" }}{PARA 12 "" 1 "" {XPPMATH 
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F6F+F6F:F6F1F6F***FBF6F-F6F0F6F1F6F***FBF6F:F6F7F6F8F6F***FBF6F0F6F8F6
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