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 A244393 Number of partitions of n the largest part of which, call it m, appears once, m-1 appears at most twice, m-2 appears at most thrice, etc. 2
 1, 1, 1, 2, 3, 4, 6, 9, 13, 17, 25, 33, 45, 61, 82, 106, 142, 183, 238, 306, 395, 499, 638, 804, 1014, 1268, 1586, 1967, 2447, 3018, 3721, 4566, 5598, 6827, 8328, 10108, 12257, 14812, 17884, 21508, 25856, 30980, 37076, 44261, 52776, 62768, 74578, 88407, 104681, 123703, 146018, 172019, 202445, 237830, 279087, 326991, 382706 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 EXAMPLE For n=6 the partitions counted are 6, 51, 42, 411, 321, 3111 The a(9) = 17 such partitions of 9 are: 01: [ 3 2 2 1 1 ] 02: [ 4 2 1 1 1 ] 03: [ 4 2 2 1 ] 04: [ 4 3 1 1 ] 05: [ 4 3 2 ] 06: [ 5 1 1 1 1 ] 07: [ 5 2 1 1 ] 08: [ 5 2 2 ] 09: [ 5 3 1 ] 10: [ 5 4 ] 11: [ 6 1 1 1 ] 12: [ 6 2 1 ] 13: [ 6 3 ] 14: [ 7 1 1 ] 15: [ 7 2 ] 16: [ 8 1 ] 17: [ 9 ] MAPLE b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, `if`(t=1, 1, t+1))+add( b(n-i*j, i-1, t+1), j=1..min(t, n/i)))) end: a:= n-> b(n\$2, 1): seq(a(n), n=0..60); # Alois P. Heinz, Jul 29 2017 MATHEMATICA nend=20; For[n=1, n<=nend, n++, count[n]=0; Ip=IntegerPartitions[n]; For[i=1, i<=Length[Ip], i++, m=Max[Ip[[i]]]; condition=True; Tip=Tally[Ip[[i]]]; For[j=1, j<=Length[Tip], j++, condition=condition&&(Tip[[j]][[2]]<= m-Tip[[j]][[1]]+1)]; If[condition, count[n]++(*; Print[Ip[[i]]]*)]]; ] Table[count[i], {i, 1, nend}] (* Second program: *) b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, If[t == 1, 1, t + 1]] + Sum[ b[n - i*j, i - 1, t + 1], {j, 1, Min[t, n/i]}]]]; a[n_] := b[n, n, 1]; a /@ Range[0, 60] (* Jean-François Alcover, Jun 05 2021, after Alois P. Heinz *) CROSSREFS Cf. A244395. Sequence in context: A240079 A240727 A123648 * A286929 A255525 A129632 Adjacent sequences: A244390 A244391 A244392 * A244394 A244395 A244396 KEYWORD nonn AUTHOR David S. Newman, Jul 03 2014 EXTENSIONS More terms from Joerg Arndt, Jul 03 2014 STATUS approved

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Last modified September 8 22:43 EDT 2024. Contains 375759 sequences. (Running on oeis4.)