A380580 Irregular tetrahedron T(s,r,k) read by rows in which the slice s is an irregular triangle, itself read by rows, in which row r lists the r-th row of A237593 sandwiched between two A380579(s+1,r+1), with s >= 0; 0 <= r <= s; k >= 0. Assume that row 0 of A237593 is empty.
1, 1, 2, 2, 1, 1, 1, 1, 4, 4, 3, 1, 1, 3, 2, 2, 2, 2, 5, 5, 4, 1, 1, 4, 3, 2, 2, 3, 2, 2, 1, 1, 2, 2, 7, 7, 6, 1, 1, 6, 5, 2, 2, 5, 4, 2, 1, 1, 2, 4, 3, 3, 1, 1, 3, 3, 8, 8, 7, 1, 1, 7, 6, 2, 2, 6, 5, 2, 1, 1, 2, 5, 4, 3, 1, 1, 3, 4, 3, 3, 2, 2, 3, 3, 10, 10, 9, 1, 1, 9, 8, 2, 2, 8, 7, 2, 1, 1, 2, 7, 6, 3, 1, 1, 3, 6, 5, 3, 2, 2, 3, 5
Offset: 0
Links
- Paolo Xausa, Table of n, a(n) for n = 0..14441 (slices 0..50 of the tetrahedron, flattened).
- Omar E. Pol, Discussion of the Sequence A380580.
- Omar E. Pol, Illustration of initial terms of A000203 in the pyramid.
- Omar E. Pol, Illustration of initial terms of A001065 in the pyramid.
- Omar E. Pol, Illustration of initial terms of A048050 in the pyramid.
- Omar E. Pol, Illustration of initial terms of A067742 in the pyramid.
- Omar E. Pol, Illustration of initial terms of A224613 (black spiders).
- Omar E. Pol, Illustration of initial terms of A237593 (essentially a template for the Pop-Up pyramid).
- Omar E. Pol, Prism of partitions of 10 and its companion tower (both have the same volume).
- Omar E. Pol, The symmetric representation of sigma(n), n = 1..64 (the top view of the pyramid and of the tower).
Crossrefs
See the "Discussion" text file for the cross-references.
Programs
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Mathematica
A237593row[n_] := Join[#, Reverse[#]] & [Table[Ceiling[(n+1)/k - (k+1)/2] + Quotient[k*(k+3) - 2*n, 2*(k+1)], {k, Quotient[Sqrt[8*n + 1] - 1, 2]}]]; A380580slice[s_] := Table[Join[#, A237593row[r], #] & [{Quotient[3*s, 2] - r + 1}], {r, 0, s}]; Array[A380580slice, 10, 0] (* Paolo Xausa, Aug 19 2025 *)
Extensions
Edited by N. J. A. Sloane, Jul 31 2025
Comments