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EXAMPLE
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The initial nodes of the sub-Fibonacci tree for generations 0..5 are:
gen.0: [1];
gen.1: [2];
gen.2: [3];
gen.3: [4,5];
gen.4: (4)->[5,6,7],(5)->[6,7,8];
gen.5: (5)->[6,7,8,9],(6)->[7,8,9,10],(7)->[8,9,10,11],
(6)->[7,8,9,10,11],(7)->[8,9,10,11,12],(8)->[9,10,11,12,13].
The sum of the labels for nodes in generation n+1 >= 2 is equal to:
a(n+1) = sum (parent label)*(label) over all nodes in generation n + sum (parent label)*[label*(label+1)/2] over all nodes in gen. n-1.
For example:
a(2) = 3 = 1*2 + 1*( 1*2/2 );
a(3) = 9 = 2*3 + 1*( 2*3/2 );
a(4) = 39 = 3*(4+5) + 2*( 3*4/2 );
a(5) = 252 = 4*(5+6+7) + 5*(6+7+8) + 3*( 4*5/2 + 5*6/2 );
a(6) = 2361 = 5*(6+7+8+9) + 6*(7+8+9+10) + 7*(8+9+10+11) +
6*(7+8+9+10+11) + 7*(8+9+10+11+12) + 8*(9+10+11+12+13) +
4*( 5*6/2 + 6*7/2 + 7*8/2 ) + 5*( 6*7/2 + 7*8/2 + 8*9/2 ).
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