Hugo Pfoertner wrote:

Paul, SeqFans,

Donald E. Knuth describes an efficient method to construct the power
tree in "Answers to exercises"  for Section 4.6.3 page 692, exercise 5
is given on page 481 TAOCP Vol. 2.

I wrote a small Fortran program implementing Knuth's algorithm:

http://www.randomwalk.de/sequences/pwrtree.txt
producing the following results in a few CPU seconds:

level  leftmost  number      row sums
       node in   of nodes
       row       in row
  2       2       1              2
  3       3       2              7
  4       5       3             19
  5       7       5             54
  6      14       9            164
  7      19      15            476
  8      38      26           1417
  9      57      43           4087
 10      71      78          12589
 11     142     134          37818
 12     284     238         116828
 13     568     415         358277
 14     571     731        1106870
 15    1142    1299        3460676
 16    2284    2299       10813998
 17    4568    4126       34339769
 18    9136    7374      109194390
 19   18272   13257      350181146
 20   36544   23847     1126919513
 21   36545   42864     3634208553
 22   73089   77366    11774823887
 23  146178  140071    38335906599
 24  292356  254241   125461951555
 25  292361  461967   411934520324
 26  584722  839829  1356668825821
 27 1169444 1528072  4478273903272

Using 8 GByte of memory and a slightly modified program (64 bit row sum
accumulation) I got 4 more terms:

 28  2338888  2782636      14813386035089
 29  4677776  5076421      49127626291866
 30  9355552  9274937     163338735996170
 31 18711104 16973162     544653547399708

Paul D. Hanna will submit the corresponding sequences A114622 ... A114625

Hugo Pfoertner

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