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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.
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%I #5 Jan 24 2022 16:12:20

%S 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,

%T 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,

%U 0,0,4,5,5,4,0,0,1,0,0,1,1,0,4,5,6,5,4,0,1,1,0

%N 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.

%H Rémy Sigrist, <a href="/A350673/a350673.gp.txt">PARI program for A350673</a>

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

%F T(n, n) = n.

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

%e Array T(n, k) begins:

%e n\k| 0 1 2 3 4 5 6 7 8 9 10

%e ---+----------------------------------

%e 0| 0 0 0 0 0 0 0 0 0 0 0

%e 1| 0 1 1 1 0 1 1 1 0 0 1

%e 2| 0 1 2 2 0 1 2 2 0 0 1

%e 3| 0 1 2 3 0 1 2 3 0 0 1

%e 4| 0 0 0 0 4 4 4 4 4 0 0

%e 5| 0 1 1 1 4 5 5 5 4 0 1

%e 6| 0 1 2 2 4 5 6 6 4 0 1

%e 7| 0 1 2 3 4 5 6 7 4 0 1

%e 8| 0 0 0 0 4 4 4 4 8 0 0

%e 9| 0 0 0 0 0 0 0 0 0 9 9

%e 10| 0 1 1 1 0 1 1 1 0 9 10

%o (PARI) See Links section.

%Y Cf. A350674.

%K nonn,tabl

%O 0,13

%A _Rémy Sigrist_, Jan 10 2022