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A277437 Square array read by antidiagonals upwards in which T(n,k) is the n-th number j such that, descending by the main diagonal of the pyramid described in A245092, the height difference between the level j (starting from the top) and the level of the next terrace is equal to k.

%I A277437 #64 Dec 31 2020 11:11:15
%S A277437 1,3,2,5,4,9,7,6,12,20,8,10,21,36,72,11,13,25,50,91,144,14,16,32,56,
%T A277437 112
%N A277437 Square array read by antidiagonals upwards in which T(n,k) is the n-th number j such that, descending by the main diagonal of the pyramid described in A245092, the height difference between the level j (starting from the top) and the level of the next terrace is equal to k.
%C A277437 This is a permutation of the natural numbers.
%C A277437 Column k lists the numbers with precipice k. For more information about the precipices see A280223 and A280295.
%C A277437 The structure of the stepped pyramid arises after the 90-degree-zig-zag folding of the diagram of the isosceles triangle A237593.
%C A277437 The terraces at the m-th level of the pyramid are also the parts of the symmetric representation of sigma(m), m >= 1.
%C A277437 The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.
%C A277437 If a number m is in the column k and k > 1 then m + 1 is the column k - 1.
%C A277437 The largest Dyck path of the symmetric representations of next k - 1 positive integers greater than T(n,k) shares the middle point of the largest Dyck path of the symmetric representation of sigma(T(n,k)). For more information see A237593.
%H A277437 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr05.jpg">Perspective view of the pyramid (first 16 levels)</a>
%H A277437 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A277437 T(n,1) = A071562(n+1) - 1.
%e A277437 The corner of the square array begins:
%e A277437    1,  2,  9, 20, 72, 144,
%e A277437    3,  4, 12, 36, 91,
%e A277437    5,  6, 21, 50,
%e A277437    7, 10, 25,
%e A277437    8, 13,
%e A277437   11,
%e A277437   ...
%e A277437 T(1,6) = 144 because it is the smallest number with precipice 6.
%Y A277437 Row 1 gives A280295.
%Y A277437 Column 1 gives A276112.
%Y A277437 Cf. A000203, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A240542, A244050, A245092, A259179, A262626, A279286, A279385, A280223.
%K A277437 nonn,tabl,more
%O A277437 1,2
%A A277437 _Omar E. Pol_, Dec 29 2016
%E A277437 a(20)-a(26) from _Omar E. Pol_, Jan 02 2017