A229362 a(n) = n for n = 1, 2, 3; for n > 3: a(n) = number of partitions of n into preceding terms.

1, 2, 3, 4, 6, 10, 12, 17, 21, 29, 34, 47, 55, 71, 84, 107, 124, 156, 180, 221, 256, 310, 355, 428, 488, 578, 660, 775, 879, 1027, 1160, 1342, 1516, 1743, 1958, 2243, 2513, 2858, 3198, 3621, 4037, 4556, 5065, 5689, 6316, 7069, 7824, 8733, 9644, 10726, 11827

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

a(4) = #{3+1, 2+2, 2+1+1, 1+1+1+1} = 4 < A000041(4) = 5;
a(5) = #{4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 5x1} = 6 < A000041(5) = 7;
a(6) = #{6, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+4x1, 6x1} = 10 < A000041(6) = 11;
a(7) = #{6+1, 4+3, 4+2+1, 4+1+1+1, 3+3+1, 3+2+2, 3+2+1+1, 3+4x1, 2+2+2+1, 2+2+1+1+1, 2+5x1, 7x1} = 12 < A000041(7) = 15.

Mathematica

a[n_] := a[n] = If[n<4, n, IntegerPartitions[n, All, Array[a, n-1]] // Length];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 12 2019 *)

Prog

(Haskell)
a229362 n = a229362_list !! (n-1)
a229362_list = 1 : 2 : 3 : f 4 [1, 2, 3] where
   f x ys = y : f (x + 1) (ys ++ [y]) where y = p ys x
   p _          0 = 1
   p []         _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

Crossrefs

Cf. A000041, A007279.

Sequence in context: A068499 A137172 A069744 * A249685 A343731 A181312

Adjacent sequences: A229359 A229360 A229361 * A229363 A229364 A229365

Keyword

nonn

Author

Reinhard Zumkeller, Sep 21 2013

Status

approved