A350674 Irregular table read by rows; the n-th row contains, in weakly decreasing order, the positive squares summing to n as obtained by the greedy algorithm.

1, 1, 1, 1, 1, 1, 4, 4, 1, 4, 1, 1, 4, 1, 1, 1, 4, 4, 9, 9, 1, 9, 1, 1, 9, 1, 1, 1, 9, 4, 9, 4, 1, 9, 4, 1, 1, 16, 16, 1, 16, 1, 1, 16, 1, 1, 1, 16, 4, 16, 4, 1, 16, 4, 1, 1, 16, 4, 1, 1, 1, 16, 4, 4, 25, 25, 1, 25, 1, 1, 25, 1, 1, 1, 25, 4, 25, 4, 1, 25, 4, 1, 1

Offset: 1

Author

Rémy Sigrist, Jan 10 2022

Keywords

• nonn
• tabf

Comments

The n-th row has A053610(n) terms.

Examples

			The first rows are:
     1:    [1]
     2:    [1, 1]
     3:    [1, 1, 1]
     4:    [4]
     5:    [4, 1]
     6:    [4, 1, 1]
     7:    [4, 1, 1, 1]
     8:    [4, 4]
     9:    [9]
    10:    [9, 1]
    11:    [9, 1, 1]
    12:    [9, 1, 1, 1]
    13:    [9, 4]
    14:    [9, 4, 1]
    15:    [9, 4, 1, 1]
    16:    [16]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1733 (rows 1..500)

Crossrefs

Cf. A007961, A048760, A053610, A350698.

Programs

PARI

row(n,e=2) = { my (g=[], r); while (n, r=sqrtnint(n,e); n-=r^e; g=concat(g,[r^e])); g }

Formula

T(n, 1) = A048760(n).

T(n, A053610(n)) = A350698(n).