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A229362 a(n) = n for n = 1, 2, 3; for n > 3: a(n) = number of partitions of n into preceding terms. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)