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A249042
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Three-dimensional array of numbers N(r,p,m) read by triangular slices, each slice being read across rows: N(r,p,m) is the number of "r-panes in a (p,m) structure".
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1
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1, 1, 1, 2, 1, 3, 4, 1, 6, 6, 1, 6, 7, 7, 24, 18, 1, 14, 36, 24, 1, 10, 11, 25, 70, 46, 15, 100, 180, 96, 1, 30, 150, 240, 120, 1, 15, 16, 65, 165, 101, 90, 455, 690, 326, 31, 360, 1170, 1440, 600, 1, 62, 540, 1560, 1800, 720
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OFFSET
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1,4
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COMMENTS
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Three-dimensional arrays don't really work in the OEIS, but this one seems like it should be included. See Good-Tideman for precise definition.
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LINKS
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FORMULA
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There is a formula involving Stirling numbers.
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EXAMPLE
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The initial triangular slices are:
1
-
1
1 2
---
1
3 4
1 6 6
-----
1
6 7
7 24 18
1 14 36 24
----------
1
10 11
25 70 46
15 100 180 96
1 30 150 240 120
----------------
1
15 16
65 165 101
90 455 690 326
31 360 1170 1440 600
1 62 540 1560 1800 720
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MATHEMATICA
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S1[m_, n_] := Abs[StirlingS1[m, m - n]];
S2[m_, n_] := StirlingS2[m, m - n];
Nr[r_, p_, m_] := S2[m, p - r] Sum[S1[m - p + r, nu], {nu, 0, r}];
Table[Nr[r, p, m], {m, 1, 6}, {p, 0, m - 1}, {r, 0, p}] // Flatten (* Jean-François Alcover, Nov 01 2018 *)
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CROSSREFS
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The sequence of left edges of the triangles is A008278; the bases of the triangles give A019538; the hypotenuses give A181854.
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KEYWORD
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nonn,tabf,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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