Great oaks from little acorns grow

[Eugene McDonnell]

Beginning with
0 0 1 1 2 2 3 3 4 4 5 5
If we repeatedly obtain the cumulative sums we get
0 0 1  1   2   2    3     3     4      4     A004526
0 0 1  2   4   6    9    12    16     20     A002620
0 0 1  3   7  13   22    34    50     70     A002623
0 0 1  4  11  24   46    80   130    200     A001752
0 0 1  5  16  40   86   166   296    496     A001753
0 0 1  6  22  62  148   314   610   1106     A001769
0 0 1  7  29  91  239   553  1163   2269     A001779
0 0 1  8  37 128  367   920  2083   4352     A001780
0 0 1  9  46 174  541  1461  3544   7896     A001781
0 0 1 10  56 230  771  2232  5776  13672     A001786
0 0 1 11  67 297 1068  3300  9076  22748     A001808
0 0 1 12  79 376 1444  4744 13820  36568
0 0 1 13  92 468 1912  6656 20476  57044
0 0 1 14 106 574 2486  9142 29618  86662
0 0 1 15 121 695 3181 12323 41941 128603
...
Column 4 (2 4 7 11 16...) is A000124
Column 5 (2 6 13 24 40...) is A003600

Beginning with
1 1 3 3 6 6 10 10 15 15
If we repeatedly obtain the cumulative sums we get
1  1   3   3    6     6    10     10     15      15    A008805
1  2   5   8   14    20    30     40     55      70    A006918
1  3   8  16   30    50    80    120    175     245    A002624
1  4  12  28   58   108   188    308    483     728    A028346
1  5  17  45  103   211   399    707   1190    1918
1  6  23  68  171   382   781   1488   2678    4596
1  7  30  98  269   651  1432   2920   5598   10194
1  8  38 136  405  1056  2488   5408  11006   21200
1  9  47 183  588  1644  4132   9540  20546   41746
1 10  57 240  828  2472  6604  16144  36690   78436
1 11  68 308 1136  3608 10212  26356  63046  141482
1 12  80 388 1524  5132 15344  41700 104746  246228
1 13  93 481 2005  7137 22481  64181 168927  415155
1 14 107 588 2593  9730 32211  96392 265319  680474
1 15 122 710 3303 13033 45244 141636 406955 1087429
Column 2 (3 5 8 12...) is A095173

-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: text/enriched
Size: 2001 bytes
Desc: not available
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20041228/f26ae2df/attachment.bin>