cp's OEIS Frontend

A100881 Number of partitions of n in which the sequence of frequencies of the summands is decreasing.

%I A100881 #18 Jul 15 2015 09:56:45
%S A100881 1,1,2,2,3,3,4,4,6,5,7,8,8,9,13,10,13,15,16,18,21,17,24,28,26,26,36,
%T A100881 32,38,42,40,46,52,48,63,63,59,63,85,77,81,92,89,102,116,98,122,134,
%U A100881 130,140,157,145,165,182,190,191,207,195,235,259,232,252,293,279
%N A100881 Number of partitions of n in which the sequence of frequencies of the summands is decreasing.
%H A100881 Alois P. Heinz, <a href="/A100881/b100881.txt">Table of n, a(n) for n = 0..1000</a>
%e A100881 a(7) = 4 because in each of the four partitions [7], [3,3,1], [2,2,2,1], [1,1,1,1,1,1,1] the frequency with which a summand is used decreases as the summand decreases.
%p A100881 b:= proc(n, i, t) option remember;
%p A100881       if n<0 then 0
%p A100881     elif n=0 then 1
%p A100881     elif i=0 then 0
%p A100881     else      b(n, i-1, t)
%p A100881          +add(b(n-i*j, i-1, j), j=1..min(t-1, floor(n/i)))
%p A100881       fi
%p A100881     end:
%p A100881 a:= n-> b(n, n, n+1):
%p A100881 seq(a(n), n=0..60);  # _Alois P. Heinz_, Feb 21 2011
%t A100881 b[n_, i_, t_] := b[n, i, t] = Which[n<0, 0, n==0, 1, i==0, 0, True, b[n, i-1, t] + Sum[b[n-i*j, i-1, j], {j, 1, Min[t-1, Floor[n/i]]}]]; a[n_] := b[n, n, n+1]; Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Jul 15 2015, after _Alois P. Heinz_ *)
%o A100881 (Haskell)
%o A100881 a100881 = p 0 0 1 where
%o A100881    p m m' k x | x == 0    = if m > m' || m == 0 then 1 else 0
%o A100881               | x < k     = 0
%o A100881               | m == 0    = p 1 m' k (x - k) + p 0 m' (k + 1) x
%o A100881               | otherwise = p (m + 1) m' k (x - k) +
%o A100881                             if m > m' then p 0 m (k + 1) x else 0
%o A100881 -- _Reinhard Zumkeller_, Dec 27 2012
%Y A100881 Cf. A100882, A100883, A100884.
%Y A100881 Cf. A100471, A098859.
%K A100881 nonn
%O A100881 0,3
%A A100881 _David S. Newman_, Nov 21 2004
%E A100881 More terms from _Alois P. Heinz_, Feb 21 2011