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 A182410 Number of length sets of integer partitions of n. 2
 1, 1, 2, 2, 4, 4, 7, 7, 11, 11, 15, 17, 24, 25, 31, 34, 45, 48, 59, 64, 77, 83, 99, 109, 131, 138, 164, 175, 204, 222, 252, 274, 317, 332, 385, 403, 466, 500, 563, 592, 674, 720, 799, 854, 957, 994, 1131, 1196, 1328, 1395, 1551, 1627, 1817, 1912, 2098, 2197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For an integer partition n = c(1)*1 + c(2)*2 + ... + c(n)*n, construct the set of all positive c(i) occurring at least one time. a(n) is the number of distinct such sets in all integer partitions of n. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..170 EXAMPLE For n=8 the 11 possible sets are {1}, {2}, {4}, {8}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 3} and {2, 4}. MAPLE b:= proc(n, i) option remember; `if`(n=0, {{}}, `if`(i=1, {{n}}, {b(n, i-1)[], seq(map(x-> {x[], j}, b(n-i*j, i-1))[], j=1..n/i)})) end: a:= n-> nops(b(n, n)): seq(a(n), n=0..50); # Alois P. Heinz, Aug 09 2012 MATHEMATICA Table[Length@ Union@ Map[Union@(Length /@ Split[#]) &, IntegerPartitions[n]], {n, 1, 20}] PROG (Python) from sympy.utilities.iterables import partitions def A182410(n): return len({tuple(sorted(set(p.values()))) for p in partitions(n)}) # Chai Wah Wu, Sep 10 2023 CROSSREFS Cf. A000041 (number of partitions). Cf. A088314 (number of different ordered lists of the c(i)). Cf. A088887 (number of different sorted lists of the c(i)). Sequence in context: A230167 A060028 A341951 * A341719 A099770 A099383 Adjacent sequences: A182407 A182408 A182409 * A182411 A182412 A182413 KEYWORD nonn AUTHOR Olivier Gérard, May 09 2012 STATUS approved

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Last modified August 7 21:19 EDT 2024. Contains 375017 sequences. (Running on oeis4.)