A350673 Square array read by antidiagonals T(n, k), n, k >= 0; T(n, k) is the sum of the elements of the intersection of the multisets of positive squares summing to n and k, respectively, obtained by the greedy algorithm.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 4, 1, 2, 1, 0, 0, 0, 2, 2, 4, 4, 2, 2, 0, 0, 0, 0, 0, 3, 4, 5, 4, 3, 0, 0, 0, 0, 1, 0, 0, 4, 5, 5, 4, 0, 0, 1, 0, 0, 1, 1, 0, 4, 5, 6, 5, 4, 0, 1, 1, 0

Offset

0,13

Links

Table of n, a(n) for n=0..90.

Rémy Sigrist, PARI program for A350673

Formula

T(n, k) = T(k, n).

T(n, n) = n.

T(n, 0) = T(0, k) = 0.

Example

Array T(n, k) begins:
  n\k|  0  1  2  3  4  5  6  7  8  9  10
  ---+----------------------------------
    0|  0  0  0  0  0  0  0  0  0  0   0
    1|  0  1  1  1  0  1  1  1  0  0   1
    2|  0  1  2  2  0  1  2  2  0  0   1
    3|  0  1  2  3  0  1  2  3  0  0   1
    4|  0  0  0  0  4  4  4  4  4  0   0
    5|  0  1  1  1  4  5  5  5  4  0   1
    6|  0  1  2  2  4  5  6  6  4  0   1
    7|  0  1  2  3  4  5  6  7  4  0   1
    8|  0  0  0  0  4  4  4  4  8  0   0
    9|  0  0  0  0  0  0  0  0  0  9   9
   10|  0  1  1  1  0  1  1  1  0  9  10

Prog

(PARI) See Links section.

Crossrefs

Cf. A350674.

Sequence in context: A356325 A073253 A004198 * A324351 A116402 A093323

Adjacent sequences: A350670 A350671 A350672 * A350674 A350675 A350676

Keyword

nonn,tabl

Author

Rémy Sigrist, Jan 10 2022

Status

approved