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Task/Paraffins/Tcl/paraffins.tcl

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+package require Tcl 8.5
+
+set maxN 200
+set rooted [lrepeat $maxN 0]
+lset rooted 0 1; lset rooted 1 1
+set unrooted $rooted
+
+proc choose {m k} {
+    if {$k == 1} {
+	return $m
+    }
+    for {set r $m; set i 1} {$i < $k} {incr i} {
+	set r [expr {$r * ($m+$i) / ($i+1)}]
+    }
+    return $r
+}
+
+proc tree {br n cnt sum l} {
+    global maxN rooted unrooted
+    for {set b [expr {$br+1}]} {$b <= 4} {incr b} {
+	set s [expr {$sum + ($b-$br) * $n}]
+	if {$s >= $maxN} return
+	set c [expr {[choose [lindex $rooted $n] [expr {$b-$br}]] * $cnt}]
+	if {$l*2 < $s} {
+	    lset unrooted $s [expr {[lindex $unrooted $s] + $c}]
+	}
+	if {$b == 4} return
+	lset rooted $s [expr {[lindex $rooted $s] + $c}]
+	for {set m $n} {[incr m -1]} {} {
+	    tree $b $m $c $s $l
+	}
+    }
+}
+
+proc bicenter {s} {
+    if {$s & 1} return
+    global unrooted rooted
+    set r [lindex $rooted [expr {$s/2}]]
+    lset unrooted $s [expr {[lindex $unrooted $s] + $r*($r+1)/2}]
+}
+
+for {set n 1} {$n < $maxN} {incr n} {
+    tree 0 $n 1 1 $n
+    bicenter $n
+    puts "${n}: [lindex $unrooted $n]"
+}