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.
Original entry on oeis.org
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
Offset: 0
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
-
T[n_, k_] := Sum[n! k!/((n - k - j)! (k - j)! j!), {j, 0, k}]
A342073
Number of n-colorings of the vertices of the 5-dimensional cross polytope such that no two adjacent vertices have the same color.
Original entry on oeis.org
0, 0, 0, 0, 0, 120, 4320, 78120, 913920, 7575120, 46751040, 224587440, 881591040, 2946869640, 8659691040, 22915652760, 55611279360, 125508233760, 266320172160, 535945217760, 1030028705280, 1901347885080, 3386866301280, 5844714201480, 9803816225280
Offset: 0
- Peter Kagey, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
-
p = ChromaticPolynomial[CompleteGraph[Table[2, 5]], x];
Table[p /. x -> n, {n, 0, 50}]
A342074
Number of n-colorings of the vertices of the 6-dimensional cross polytope such that no two adjacent vertices have the same color.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 720, 35280, 866880, 13849920, 158004000, 1347524640, 8866186560, 46496324160, 201705744240, 748737990000, 2444976293760, 7178449299840, 19276199691840, 47983899216960, 111920569776000, 246727594270080, 517702915311120, 1039979954779920
Offset: 0
- Peter Kagey, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
-
p = ChromaticPolynomial[CompleteGraph[Table[2, 6]], x];
Table[p /. x -> n, {n, 0, 50}]
A342075
Number of n-colorings of the vertices of the 7-dimensional cross polytope such that no two adjacent vertices have the same color.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 5040, 322560, 10342080, 216518400, 3261535200, 37026823680, 325474269120, 2264594492160, 12789814237200, 60389186457600, 245221330273920, 877374833287680, 2821277454690240, 8284633867238400, 22503569636419200, 57135310310453760
Offset: 0
- Peter Kagey, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
-
p = ChromaticPolynomial[CompleteGraph[Table[2, 7]], x];
Table[p /. x -> n, {n, 0, 50}]
Showing 1-4 of 4 results.