cp's OEIS Frontend

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.

%I A342128 #17 Feb 16 2025 08:34:01
%S A342128 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,
%T A342128 260,2652,2970,2,0,0,8,42,630,29660,1321860,1185282,2,0,0,9,56,1302,
%U A342128 198030,187430900,130253748108,100301050602,2,0,0,10,72,2408,932862,10199069190,2157531034816940
%N 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.
%H A342128 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChromaticPolynomial.html">Chromatic Polynomial</a>
%H A342128 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%F A342128 T(n,k) = Sum_{i=0..2^k} A334278(k,i)*n^i.
%e A342128 Table begins:
%e A342128   n\k|  0   1     2         3                4                              5
%e A342128   ---+-----------------------------------------------------------------------
%e A342128    0 |  0   0     0         0                0                              0
%e A342128    1 |  1   0     0         0                0                              0
%e A342128    2 |  2   2     2         2                2                              2
%e A342128    3 |  3   6    18       114             2970                        1185282
%e A342128    4 |  4  12    84      2652          1321860                   130253748108
%e A342128    5 |  5  20   260     29660        187430900               2157531034816940
%e A342128    6 |  6  30   630    198030      10199069190            7905235551766437150
%e A342128    7 |  7  42  1302    932862     269591166222         7365707045872206479742
%e A342128    8 |  8  56  2408   3440024    4221404762120      2337101560809838105414712
%e A342128    9 |  9  72  4104  10599192   44876701584360    327425229254999498091796728
%e A342128   10 | 10  90  6570  28478970  355148098691850  24489214732779742874109277530
%Y A342128 Columns and rows: A002378 (k=1), A091940 (k=2), A140986 (k=3), A158348 (k=4), A380589 (k=5), A307334 (n=3).
%Y A342128 Cf. A334278, A342088 (analogous for cross-polytope).
%K A342128 nonn,tabl
%O A342128 0,4
%A A342128 _Peter Kagey_, Feb 28 2021