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 A342516 Number of strict integer partitions of n with weakly increasing first quotients. 5
 1, 1, 1, 2, 2, 3, 3, 5, 5, 6, 7, 8, 8, 11, 12, 14, 15, 17, 17, 21, 22, 26, 29, 31, 32, 35, 38, 42, 45, 48, 51, 58, 59, 63, 70, 76, 80, 88, 94, 98, 105, 113, 121, 129, 133, 143, 153, 159, 166, 183, 189, 195, 210, 221, 231, 248, 262, 273, 284, 298, 312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Also called log-concave-up strict partitions. Also the number of reversed strict integer partitions of n with weakly increasing first quotients. The first quotients of a sequence are defined as if the sequence were an increasing divisor chain, so for example the first quotients of (6,3,1) are (1/2,1/3). LINKS Eric Weisstein's World of Mathematics, Logarithmically Concave Sequence. EXAMPLE The partition (6,3,2,1) has first quotients (1/2,2/3,1/2) so is not counted under a(12), even though the first differences (-3,-1,-1) are weakly increasing. The a(1) = 1 through a(13) = 11 partitions (A..D = 10..13):   1   2   3    4    5    6    7     8     9     A     B     C     D           21   31   32   42   43    53    54    64    65    75    76                     41   51   52    62    63    73    74    84    85                               61    71    72    82    83    93    94                               421   521   81    91    92    A2    A3                                           621   532   A1    B1    B2                                                 721   632   732   C1                                                       821   921   643                                                                   832                                                                   931                                                                   A21 MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&LessEqual@@Divide@@@Reverse/@Partition[#, 2, 1]&]], {n, 0, 30}] CROSSREFS The version for differences instead of quotients is A179255. The non-strict ordered version is A342492. The non-strict version is A342497 (ranking: A342523). The strictly increasing version is A342517. The weakly decreasing version is A342519. A000041 counts partitions (strict: A000009). A000929 counts partitions with all adjacent parts x >= 2y. A001055 counts factorizations (strict: A045778, ordered: A074206). A003238 counts chains of divisors summing to n - 1 (strict: A122651). A167865 counts strict chains of divisors > 1 summing to n. A342094 counts partitions with all adjacent parts x <= 2y (strict: A342095). Cf. A000005, A003114, A003242, A005117, A057567, A067824, A238710, A253249, A318991, A318992, A342528. Sequence in context: A178503 A211275 A240542 * A325391 A179254 A304430 Adjacent sequences:  A342513 A342514 A342515 * A342517 A342518 A342519 KEYWORD nonn AUTHOR Gus Wiseman, Mar 20 2021 STATUS approved

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)