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Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = A005836(n+1) + A005836(k+1).
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%I #28 Jul 21 2024 12:48:16

%S 0,1,1,3,2,3,4,4,4,4,9,5,6,5,9,10,10,7,7,10,10,12,11,12,8,12,11,12,13,

%T 13,13,13,13,13,13,13,27,14,15,14,18,14,15,14,27,28,28,16,16,19,19,16,

%U 16,28,28,30,29,30,17,21,20,21,17,30,29,30,31,31,31,31,22,22,22,22,31,31,31,31

%N Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = A005836(n+1) + A005836(k+1).

%C For any v >= 0, the value v appears A120880(v) times.

%H Rémy Sigrist, <a href="/A374560/b374560.txt">Table of n, a(n) for n = 0..8255</a> (antidiagonals for n+k = 0..127 flattened)

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

%F A(2*n, 2*k) = 3*A(n, k).

%e Array A(n, k) begins:

%e n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12

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

%e 0 | 0 1 3 4 9 10 12 13 27 28 30 31 36

%e 1 | 1 2 4 5 10 11 13 14 28 29 31 32 37

%e 2 | 3 4 6 7 12 13 15 16 30 31 33 34 39

%e 3 | 4 5 7 8 13 14 16 17 31 32 34 35 40

%e 4 | 9 10 12 13 18 19 21 22 36 37 39 40 45

%e 5 | 10 11 13 14 19 20 22 23 37 38 40 41 46

%e 6 | 12 13 15 16 21 22 24 25 39 40 42 43 48

%e 7 | 13 14 16 17 22 23 25 26 40 41 43 44 49

%e 8 | 27 28 30 31 36 37 39 40 54 55 57 58 63

%e 9 | 28 29 31 32 37 38 40 41 55 56 58 59 64

%e 10 | 30 31 33 34 39 40 42 43 57 58 60 61 66

%e 11 | 31 32 34 35 40 41 43 44 58 59 61 62 67

%e 12 | 36 37 39 40 45 46 48 49 63 64 66 67 72

%o (PARI) A(n, k) = fromdigits(binary(n), 3) + fromdigits(binary(k), 3)

%Y Cf. A005836, A120880, A374789, A374790, A374791, A374792.

%K nonn,base,tabl,easy

%O 0,4

%A _Rémy Sigrist_, Jul 20 2024