# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a304707 Showing 1-1 of 1 %I A304707 #15 Nov 23 2020 08:03:10 %S A304707 1,1,1,2,1,2,3,2,2,4,3,4,5,4,5,7,5,7,8,8,10,12,10,11,14,14,14,18,17, %T A304707 20,23,22,26,30,29,32,35,34,37,43,44,48,54,54,59,67,70,76,81,84,89,97, %U A304707 101,110,119,123,129,139,145,155,171,176,189,201,211,228,245,257,274,295 %N A304707 Number of partitions (d1,d2,...,dm) of n such that d1/1 >= d2/2 >= ... >= dm/m and d1 < d2 < ... < dm. %e A304707 n | Partition (d1,d2,...,dm) | (d1/1, d2/2, ... , dm/m) %e A304707 --+-----------------------------+------------------------- %e A304707 1 | (1) | (1) %e A304707 2 | (2) | (2) %e A304707 3 | (3) | (3) %e A304707 | (1, 2) | (1, 1) %e A304707 4 | (4) | (4) %e A304707 5 | (5) | (5) %e A304707 | (2, 3) | (2, 3/2) %e A304707 6 | (6) | (6) %e A304707 | (2, 4) | (2, 2) %e A304707 | (1, 2, 3) | (1, 1, 1) %e A304707 7 | (7) | (7) %e A304707 | (3, 4) | (3, 2) %e A304707 8 | (8) | (8) %e A304707 | (3, 5) | (3, 5/2) %e A304707 9 | (9) | (9) %e A304707 | (3, 6) | (3, 3) %e A304707 | (4, 5) | (4, 5/2) %e A304707 | (2, 3, 4) | (2, 3/2, 4/3) %p A304707 b:= proc(n, r, i, t) option remember; `if`(n=0, 1, `if`(i>n, 0, %p A304707 b(n, r, i+1, t) +`if`(i/t>r, 0, b(n-i, i/t, i+1, t+1)))) %p A304707 end: %p A304707 a:= n-> b(n$2, 1$2): %p A304707 seq(a(n), n=0..80); # _Alois P. Heinz_, May 17 2018 %t A304707 b[n_, r_, i_, t_] := b[n, r, i, t] = If[n == 0, 1, If[i > n, 0, b[n, r, i + 1, t] + If[i/t > r, 0, b[n - i, i/t, i + 1, t + 1]]]]; %t A304707 a[n_] := b[n, n, 1, 1]; %t A304707 a /@ Range[0, 80] (* _Jean-François Alcover_, Nov 23 2020, after _Alois P. Heinz_ *) %Y A304707 Cf. A053251, A053282, A304705, A304706, A304708. %K A304707 nonn %O A304707 0,4 %A A304707 _Seiichi Manyama_, May 17 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE