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

1,7

Comments

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

References

Hans Rademacher and Otto Toeplitz, The Enjoyment of Mathematics, Princeton Science Library, 1994. See p. 52.

Links

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

Formula

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

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

Example

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]

Mathematica

k=2; row[n_, k]:=Module[{r={}, d=n}, While[d>0, s=Floor[d^(1/k)]; AppendTo[r, s^k]; d-=s^k]; r]; Table[row[n, k], {n, 31}]//Flatten (* Stefano Spezia, Dec 27 2025 *)

Prog

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

Crossrefs

Cf. A007961, A048760, A053610, A350698.

Sequence in context: A138522 A095813 A010656 * A321591 A023401 A055180

Adjacent sequences: A350671 A350672 A350673 * A350675 A350676 A350677

Keyword

nonn,tabf

Author

Rémy Sigrist, Jan 10 2022

Status

approved