A287146 Number of partitions of n into distinct parts such that the absolute difference between any part and the sum of all smaller parts is not larger than one.

1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2

Offset

0,14

Links

Alois P. Heinz, Table of n, a(n) for n = 0..16384

Formula

a(2^n) = 0 for n > 0.

a(2^n-1) = 1 for n >= 0.

Example

a(3) = 1: 21.
a(13) = 2: 6421, 7321.
a(25) = 3: (12)6421, (12)7321, (13)6321.

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
      b(n, i-1)+`if`(i>n or abs(i-(n-i))>1, 0, b(n-i, i-1))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..120);

Mathematica

b[n_, i_] := b[n, i] = If[i(i+1)/2 < n, 0, If[n == 0, 1, b[n, i - 1] + If[i > n || Abs[i - (n - i)] > 1, 0, b[n - i, i - 1]]]];
a[n_] := b[n, n];
a /@ Range[0, 120] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000009, A002487, A287144.

Sequence in context: A321922 A362496 A360003 * A025926 A175134 A027355

Adjacent sequences: A287143 A287144 A287145 * A287147 A287148 A287149

Keyword

nonn,look

Author

Alois P. Heinz, May 20 2017

Status

approved