A300715 Number of compositions (ordered partitions) of n into squares that do not divide n.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 3, 0, 0, 7, 6, 0, 0, 14, 10, 4, 0, 22, 20, 10, 0, 32, 39, 20, 0, 49, 70, 42, 0, 12, 116, 88, 0, 128, 156, 174, 11, 207, 3, 320, 0, 333, 551, 575, 0, 555, 914, 0, 0, 959, 1502, 1829, 44, 1691, 2486, 3192, 0, 3000, 4172, 4005

Offset

0,14

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Example

a(21) = 4 because we have [9, 4, 4, 4], [4, 9, 4, 4], [4, 4, 9, 4] and [4, 4, 4, 9].

Maple

a:= proc(m) option remember; local b; b:= proc(n) option
      remember; `if`(n=0, 1, add((s->`if`(s>n or irem(m, s)
       =0, 0, b(n-s)))(j^2), j=2..isqrt(n))) end; b(m)
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 11 2018

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && IntegerQ[k^(1/2)]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 75}]

Crossrefs

Cf. A000290, A006456, A294105, A294265, A294266, A300702, A300703, A300704, A300706.

Sequence in context: A226728 A244140 A091227 * A035444 A376417 A376418

Adjacent sequences: A300712 A300713 A300714 * A300716 A300717 A300718

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 11 2018

Status

approved