This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A276112 #43 Mar 05 2022 00:34:00
%S A276112 1,3,5,7,8,11,14,15,17,19,23,24,27,29,31,34,35,39,41,44,47,48,49,53,
%T A276112 55,59,62,63,65,69,71,76,79,80,83,87,89,90,95,97,98,99,103,107,109,
%U A276112 111,116,119,120,125,127,129,131,134,139,142,143,149,152,153,155,159
%N A276112 Numbers with precipice 1: descending by the main diagonal of the pyramid described in A245092, the height difference between the level a(n) (starting from the top) and the level of the next terrace is equal to 1.
%C A276112 The structure of the stepped pyramid arises after the 90-degree-zig-zag folding of the diagram of the isosceles triangle A237593.
%C A276112 The terraces at the k-th level of the pyramid are also the parts of the symmetric representation of sigma(k).
%C A276112 The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.
%C A276112 For more information about the precipices see A277437, A280223 and A280295.
%C A276112 From _Hartmut F. W. Hoft_, Feb 02 2022: (Start)
%C A276112 Also partial sums of A280919.
%C A276112 a(n) is also the largest number of a Dyck path that crosses the diagonal at point A282131(n) which also is the rightmost number in each nonzero row of the irregular triangle in A279385. (End)
%H A276112 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr05.jpg">Perspective view of the stepped pyramid (first 16 levels)</a>
%F A276112 a(n) = A071562(n+1) - 1.
%F A276112 a(n) = Sum_{i=1..n} A280919(i), n >= 1. - _Hartmut F. W. Hoft_, Feb 02 2022
%e A276112 From _Hartmut F. W. Hoft_, Feb 02 2022: (Start)
%e A276112 n: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 index.
%e A276112 A282131: 1 2 3 5 6 7 9 11 12 13 15 17 18 20 position on diagonal.
%e A276112 A276112: 1 3 5 7 8 11 14 15 17 19 23 24 27 29 max index of Dyck path.
%e A276112 A280919: 1 2 2 2 1 3 3 1 2 2 4 1 3 2 paths at diag position.
%e A276112 (End)
%t A276112 (* last computed value of a280919[ ] is dropped to avoid a potential undercount of crossings *)
%t A276112 a240542[n_] := Sum[(-1)^(k+1)Ceiling[(n+1)/k-(k+1)/2], {k, 1, Floor[-1/2+1/2 Sqrt[8n+1]]}]
%t A276112 a280919[n_] := Most[Map[Length, Split[Map[a240542, Range[n]]]]]
%t A276112 A276112[160] (* _Hartmut F. W. Hoft_, Feb 02 2022 *)
%Y A276112 Column 1 of A277437.
%Y A276112 Cf. A000203, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A240542, A244050, A245092, A259179, A262626, A279286, A279385, A280223, A280295.
%Y A276112 Cf. A280919, A282131.
%K A276112 nonn
%O A276112 1,2
%A A276112 _Omar E. Pol_, Jan 02 2017