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

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

Offset

0,3

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).

Formula

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

Maple

a:= n-> (((((((((((((((((((((((((((((((n-80)*n+3160)*n-82080)*n+1575420)*n
    -23805776)*n+294640000)*n-3068289720)*n+27406254870)*n-212981036784)*n
    +1455643449120)*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);

Crossrefs

Column k=5 of A342128.

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

Sequence in context: A051118 A324439 A218169 * A168535 A303433 A253264

Adjacent sequences: A380586 A380587 A380588 * A380590 A380591 A380592

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 27 2025

Status

approved