login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A342088 Triangle read by rows: T(n,k) is the number of n-colorings of the vertices of the k-dimensional cross polytope such that no two adjacent vertices have the same color. 0 <= k <= n. 5
1, 1, 1, 1, 4, 2, 1, 9, 18, 6, 1, 16, 84, 96, 24, 1, 25, 260, 780, 600, 120, 1, 36, 630, 4080, 7560, 4320, 720, 1, 49, 1302, 15330, 61320, 78120, 35280, 5040, 1, 64, 2408, 45696, 351120, 913920, 866880, 322560, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Peter Kagey, Rows n = 0..100, flattened

Eric Weisstein's World of Mathematics, Chromatic Polynomial

Eric Weisstein's World of Mathematics, Cocktail Party Graph

Wikipedia, Cross-polytope

Wikipedia, TurĂ¡n graph

FORMULA

T(n,n) = n!.

T(n,k) = Sum_{i=0..2*k} A334279(k,i)*n^i.

T(n,k) = n*T(n-1,k-1) + n*(n-1)*T(n-2,k-1).

T(n,k) = Sum_{j=0..k} n!k!/((n-k-j)!(k-j)!j!).

EXAMPLE

Triangle begins:

  n\k| 0   1     2      3       4       5       6       7      8

  ---+----------------------------------------------------------

   0 | 1

   1 | 1,  1

   2 | 1,  4,    2

   3 | 1,  9,   18,     6

   4 | 1, 16,   84,    96,     24

   5 | 1, 25,  260,   780,    600,    120

   6 | 1, 36,  630,  4080,   7560,   4320,    720

   7 | 1, 49, 1302, 15330,  61320,  78120,  35280,   5040

   8 | 1, 64, 2408, 45696, 351120, 913920, 866880, 322560, 40320

MATHEMATICA

T[n_, k_] := Sum[n! k!/((n - k - j)! (k - j)! j!), {j, 0, k}]

CROSSREFS

Cf. A000012 (k=0), A000290 (k=1), A091940 (k=2), A115400 (k=3), A334281 (k=4), A342073 (k=5), A342074 (k=6), A342075 (k=7).

Cf. A334279.

Sequence in context: A259985 A144084 A021010 * A193607 A075397 A049429

Adjacent sequences:  A342085 A342086 A342087 * A342089 A342090 A342091

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Feb 27 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 07:26 EDT 2021. Contains 343146 sequences. (Running on oeis4.)