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A331884 Number of compositions (ordered partitions) of n^2 into distinct squares. 3
1, 1, 1, 1, 1, 3, 1, 7, 1, 31, 123, 151, 121, 897, 7351, 5415, 14881, 48705, 150583, 468973, 1013163, 1432471, 1730023, 50432107, 14925241, 125269841, 74592537, 241763479, 213156871, 895153173, 7716880623, 2681163865, 3190865761, 22501985413, 116279718801 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

FORMULA

a(n) = A331844(A000290(n)).

EXAMPLE

a(5) = 3 because we have [25], [16, 9] and [9, 16].

MAPLE

b:= proc(n, i, p) option remember;

      `if`(i*(i+1)*(2*i+1)/6<n, 0, `if`(n=0, p!,

      `if`(i^2>n, 0, b(n-i^2, i-1, p+1))+b(n, i-1, p)))

    end:

a:= n-> b(n^2, n, 0):

seq(a(n), n=0..35);  # Alois P. Heinz, Jan 30 2020

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = If[i(i+1)(2i+1)/6 < n, 0, If[n == 0, p!, If[i^2 > n, 0, b[n - i^2, i - 1, p + 1]] + b[n, i - 1, p]]];

a[n_] := b[n^2, n, 0];

a /@ Range[0, 35] (* Jean-Fran├žois Alcover, Nov 08 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000290, A006456, A030273, A032020, A037444, A105152, A224366, A232173, A280129, A298640, A331844.

Sequence in context: A290678 A290422 A278954 * A146430 A146281 A146265

Adjacent sequences:  A331881 A331882 A331883 * A331885 A331886 A331887

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 30 2020

EXTENSIONS

a(24)-a(34) from Alois P. Heinz, Jan 30 2020

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)