A380589 Number of n-colorings of the Hypercube Graph Q5.

0, 0, 2, 1185282, 130253748108, 2157531034816940, 7905235551766437150, 7365707045872206479742, 2337101560809838105414712, 327425229254999498091796728, 24489214732779742874109277530, 1119349138930999380736025706650, 34471067091433681765512048700932

Offset: 0

Author

Alois P. Heinz, Jan 27 2025

Keywords

• nonn
• easy

Comments

The Hypercube Graph Q5 has 32 vertices and 80 edges.

All terms are even.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Hypercube Graph
• Eric Weisstein's World of Mathematics, Chromatic Polynomial
• Index entries for linear recurrences with constant coefficients, signature (33, -528, 5456, -40920, 237336, -1107568, 4272048, -13884156, 38567100, -92561040, 193536720, -354817320, 573166440, -818809200, 1037158320, -1166803110, 1166803110, -1037158320, 818809200, -573166440, 354817320, -193536720, 92561040, -38567100, 13884156, -4272048, 1107568, -237336, 40920, -5456, 528, -33, 1).

Crossrefs

Column k=5 of A342128.

Cf. A001477, A002378, A091940, A140986, A158348, A334278.

Programs

Maple

a:= n-> (((((((((((((((((((((((((((((((n-80)*n+3160)*n-82080)*n+1575420)*n
    -23805776)*n+294640000)*n-3068289720)*n+27406254870)*n-212981036784)*n
    [phone])*n-8822129447280)*n+47712047044920)*n-231347639674200)*n
    +1009138022379076)*n-3968583456247214)*n+14086095737441185)*n-45124968898112160)*n
    +130327084318442384)*n-338572422663483544)*n+788328935798745052)*n
    -1636781898149840504)*n+3009654466362869780)*n-4856773984500880124)*n
    +6797172300402030636)*n-8122089299204814072)*n+8114599308192145448)*n
    -6584797184952049568)*n+4160914137061367054)*n-1915734714629493936)*n
    +569711421560808713)*n-81768640551939777)*n:
seq(a(n), n=0..12);

Formula

a(n) = n^32 - 80*n^31 + 3160*n^30 - ... (see Maple program).