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 A244395 Number of partitions of n in which the largest summand has frequency 1, the next largest summand has frequency at most 2, the third largest has frequency at most 3, etc. 3
 1, 1, 1, 2, 3, 4, 5, 8, 11, 15, 20, 26, 34, 46, 59, 78, 101, 129, 163, 209, 261, 329, 412, 517, 641, 798, 986, 1216, 1493, 1829, 2229, 2721, 3303, 4000, 4841, 5841, 7034, 8458, 10144, 12137, 14512, 17306, 20596, 24483, 29045, 34391, 40680, 48032, 56627, 66666 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2000 EXAMPLE For n=6 the partitions counted are: 6, 51, 42, 411, 321. MAPLE b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, t) +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 03 2014 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]] <= j)]; 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, t] + 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 06 2021, after Alois P. Heinz *) CROSSREFS Cf. A100471, A100883, A244393, A295261. Sequence in context: A207890 A008825 A261629 * A271488 A333347 A302592 Adjacent sequences: A244392 A244393 A244394 * A244396 A244397 A244398 KEYWORD nonn AUTHOR David S. Newman, Jul 03 2014 EXTENSIONS More terms from Alois P. Heinz, Jul 03 2014 STATUS approved

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Last modified September 10 18:00 EDT 2024. Contains 375792 sequences. (Running on oeis4.)