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A342128
Table read by antidiagonals upwards: T(n,k) is the number of n-colorings of the vertices of the k-dimensional hypercube such that no two adjacent vertices have the same color. n >= 0, k >=0.
0
0, 1, 0, 2, 0, 0, 3, 2, 0, 0, 4, 6, 2, 0, 0, 5, 12, 18, 2, 0, 0, 6, 20, 84, 114, 2, 0, 0, 7, 30, 260, 2652, 2970, 2, 0, 0, 8, 42, 630, 29660, 1321860, 1185282, 2, 0, 0, 9, 56, 1302, 198030, 187430900, 130253748108, 100301050602, 2, 0, 0, 10, 72, 2408, 932862, 10199069190, 2157531034816940
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Chromatic Polynomial
Eric Weisstein's World of Mathematics, Hypercube Graph
FORMULA
T(n,k) = Sum_{i=0..2^k} A334278(k,i)*n^i.
EXAMPLE
Table begins:
n\k| 0 1 2 3 4 5
---+-----------------------------------------------------------------------
0 | 0 0 0 0 0 0
1 | 1 0 0 0 0 0
2 | 2 2 2 2 2 2
3 | 3 6 18 114 2970 1185282
4 | 4 12 84 2652 1321860 130253748108
5 | 5 20 260 29660 187430900 2157531034816940
6 | 6 30 630 198030 10199069190 7905235551766437150
7 | 7 42 1302 932862 269591166222 7365707045872206479742
8 | 8 56 2408 3440024 4221404762120 2337101560809838105414712
9 | 9 72 4104 10599192 44876701584360 327425229254999498091796728
10 | 10 90 6570 28478970 355148098691850 24489214732779742874109277530
CROSSREFS
Columns and rows: A002378 (k=1), A091940 (k=2), A140986 (k=3), A158348 (k=4), A307334 (n=3).
Cf. A334278, A342088 (analogous for cross-polytope).
Sequence in context: A259827 A143161 A225853 * A330463 A142886 A374019
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Feb 28 2021
STATUS
approved