A374361 - OEIS

%I #10 Jul 09 2024 02:21:33

%S 0,0,1,1,0,3,0,1,3,4,1,4,3,3,4,4,0,9,0,1,9,10,1,10,0,3,9,12,0,1,3,4,9,

%T 10,12,13,1,4,10,13,3,12,3,4,12,13,4,13,9,9,10,10,9,12,9,10,12,13,10,

%U 13,12,12,13,13,0,27,0,1,27,28,1,28,0,3,27,30,0,1,3,4,27,28,30,31

%N Irregular table T(n, k), n >= 0, 0 <= k < A120880(n), read by rows; the n-th row contains the terms t of A005836 such that n - t also belongs to A005836.

%C In other words, we partition n into pairs of terms of A005836 and list the corresponding terms to get the n-th row.

%H Rémy Sigrist, <a href="/A374361/b374361.txt">Table of n, a(n) for n = 0..4095</a> (rows for n = 0..3^6-1 flattened)

%F T(n, 0) = 0 iff n belongs to A005836.

%F T(n, k) + T(n, A120880(k)-1-k) = n.

%F T(n, 0) = A374362(n).

%F T(n, A120880(k)-1) = A374363(n).

%e Triangle T(n, k) begins:

%e   n   n-th row

%e   --  -----------

%e    0  0

%e    1  0, 1

%e    2  1

%e    3  0, 3

%e    4  0, 1, 3, 4

%e    5  1, 4

%e    6  3

%e    7  3, 4

%e    8  4

%e    9  0, 9

%e   10  0, 1, 9, 10

%e   11  1, 10

%e   12  0, 3, 9, 12

%o (PARI) row(n) = { my (r = [0], t = 1, d); while (n, d = n % 3; n \= 3; if (d==1, r = concat(r, [v + t | v <- r]), d==2, r = [v + t | v <- r]); t *= 3;); return (r); }

%Y See A374354 for a similar sequence.

%Y Cf. A005836, A120880, A374362, A374363.

%K nonn,base,tabf

%O 0,6

%A _Rémy Sigrist_, Jul 06 2024