A342128 - OEIS

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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, 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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..60.

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

Adjacent sequences: A342125 A342126 A342127 * A342129 A342130 A342131

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Feb 28 2021

STATUS

approved