A287144 Number of partitions of n such that the absolute difference between any part i and the sum of all other parts not larger than i is not larger than two.

1, 1, 2, 2, 4, 4, 7, 6, 10, 8, 15, 11, 17, 13, 23, 16, 24, 18, 33, 23, 34, 26, 43, 28, 41, 30, 53, 36, 52, 39, 63, 40, 58, 42, 75, 51, 74, 56, 90, 57, 83, 60, 103, 69, 97, 71, 112, 69, 99, 71, 124, 83, 119, 89, 141, 88, 127, 91, 154, 102, 142, 103, 161, 98

Offset

0,3

Links

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

Formula

a(2^n-1) = A265278(n) for n>0.

a(2^n) = A052542(n).

a(2^n+1) = A182780(n-1) for n>0.

Example

a(7) = 6: 31111, 3211, 322, 331, 4111, 421.
a(8) = 10: 32111, 3221, 3311, 332, 41111, 4211, 422, 431, 5111, 521.
a(9) = 8: 42111, 4221, 4311, 432, 51111, 5211, 522, 531.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(i>n or abs(i-(n-i))>2, 0, b(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..100);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n || Abs[i - (n - i)] > 2, 0, b[n - i, i]]]];
a[n_] := b[n, n];
a /@ Range[0, 100] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Cf. A002487, A052542, A182780, A265278, A287146.

Sequence in context: A219027 A341949 A338333 * A348543 A085893 A341950

Adjacent sequences: A287141 A287142 A287143 * A287145 A287146 A287147

Keyword

nonn,look

Author

Alois P. Heinz, May 20 2017

Status

approved