A161923
Numbers n with property that each number corresponds to one of the partitions described in sequence A160643 and counted in A161921.
Original entry on oeis.org
28, 52, 58, 100, 106, 118, 112, 116, 124, 196, 202, 214, 238, 208, 212, 220, 226, 234, 250, 388, 394, 406, 430, 478, 232, 244, 400, 404, 412, 418, 426, 442, 454, 470, 502, 772, 778, 790, 814, 862, 958
Offset: 1
The numbers form an irregular table with shape A161921 as follows:
28
52 58
100 106 118
112 116 124 196 202 214 238
208 212 220 226 234 250 388 394 406 430 478
A125106 (Describes the mapping to partitions)
A160644
First of two sequences bisecting the second differences of the partition numbers (see A053445).
Original entry on oeis.org
1, 1, 2, 3, 4, 7, 10, 14, 22, 32, 45, 67, 95, 134, 192, 269, 373, 521, 718, 983, 1346, 1827, 2465, 3323, 4449, 5929, 7882, 10426, 13735, 18047, 23613, 30788, 40034, 51877, 67013, 86341, 110905, 142063, 181529, 231340, 294077, 372977, 471908, 595725, 750432
Offset: 1
A053445 begins
1 0 1 0 2 0 3 1 4 2 7 3 10 7 14 11 22 17 32 28 45 ...
therefore a(n) begins
1 1 2 3 4 7 10 14 22 32 45 67 95 134 192 ...
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Take[Differences[PartitionsP[Range[0,100]],2],{1,-1,2}] (* Harvey P. Dale, Aug 05 2019 *)
A160643
Bisect A053445 then calculate the first differences of the resulting sequence.
Original entry on oeis.org
0, 0, 0, 1, 1, 1, 4, 4, 6, 11, 15, 20, 33, 43, 60, 88, 119, 160, 226, 300, 404, 549, 727, 961, 1283, 1680, 2201, 2887, 3750, 4857, 6301, 8105, 10410, 13357, 17050, 21714, 27625, 34992, 44240, 55840, 70261, 88220, 110600, 138274, 172558, 214984, 267234
Offset: 1
A161921 begins: 0, 0, 1, 2, 3, 7, 11, 17, 28, 43, 63, 96, 139, 199, 287, 406, 566, ...
Therefore a(n) begins 0, 0, 0, 1, 1, 1, 4, 4, 6, ..., counting 333; 3332; 33322; 555, 4443, 333222, 33333; etc.
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Join[{0},Differences[Take[Differences[Table[PartitionsP[n],{n,0,100}],2],{2,-1,2}]]] (* Harvey P. Dale, Sep 02 2013 *)
Showing 1-3 of 3 results.
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