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

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 A099026

Adjacent sequences: A342125 A342126 A342127 * A342129 A342130 A342131

Keyword

nonn,tabl

Author

Peter Kagey, Feb 28 2021

Status

approved