

A249042


Threedimensional 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 "rpanes in a (p,m) structure".


1



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

1,4


COMMENTS

Threedimensional arrays don't really work in the OEIS, but this one seems like it should be included. See GoodTideman for precise definition.


LINKS

Table of n, a(n) for n=1..56.
I. J. Good, T. N. Tideman, Stirling numbers and a geometric structure from voting theory, Journal of Combinatorial Theory, Series A Volume 23, Issue 1, July 1977, Pages 3445.
Warren D. Smith, Ddimensional orderings and Stirling numbers, October 2014.


FORMULA

There is a formula involving Stirling numbers.


EXAMPLE

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


MATHEMATICA

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 (* JeanFrançois Alcover, Nov 01 2018 *)


CROSSREFS

The sequence of left edges of the triangles is A008278; the bases of the triangles give A019538; the hypotenuses give A181854.
Sequence in context: A060642 A306186 A154929 * A262472 A049400 A283524
Adjacent sequences: A249039 A249040 A249041 * A249043 A249044 A249045


KEYWORD

nonn,tabf,more


AUTHOR

N. J. A. Sloane, Oct 29 2014


EXTENSIONS

More terms from Michel Marcus, Aug 28 2015


STATUS

approved



