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Irregular triangle T(n, k), n > 0, k = 1..A278043(n); the n-th row contains, in ascending order, the terms in the greedy tribonacci representation of n.
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%I #10 Sep 14 2022 08:26:26

%S 1,2,1,2,4,1,4,2,4,7,1,7,2,7,1,2,7,4,7,1,4,7,13,1,13,2,13,1,2,13,4,13,

%T 1,4,13,2,4,13,7,13,1,7,13,2,7,13,1,2,7,13,24,1,24,2,24,1,2,24,4,24,1,

%U 4,24,2,4,24,7,24,1,7,24,2,7,24,1,2,7,24,4,7,24

%N Irregular triangle T(n, k), n > 0, k = 1..A278043(n); the n-th row contains, in ascending order, the terms in the greedy tribonacci representation of n.

%C See A357121 for the sequence corresponding to lazy tribonacci representations.

%H Rémy Sigrist, <a href="/A357120/a357120.gp.txt">PARI program</a>

%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>

%F T(n, 1) = A275392(n).

%F Sum_{k = 1..A278043(n)} T(n, k) = n.

%e Triangle T(n, k) begins:

%e 1: [1]

%e 2: [2]

%e 3: [1, 2]

%e 4: [4]

%e 5: [1, 4]

%e 6: [2, 4]

%e 7: [7]

%e 8: [1, 7]

%e 9: [2, 7]

%e 10: [1, 2, 7]

%e 11: [4, 7]

%e 12: [1, 4, 7]

%e 13: [13]

%e 14: [1, 13]

%e 15: [2, 13]

%o (PARI) See Links section.

%Y Cf. A000073, A035516, A035517, A275392, A278043, A278038, A357121.

%K nonn,tabf

%O 1,2

%A _Rémy Sigrist_, Sep 12 2022