A158348 Number of n-colorings of the Hypercube Graph Q4.

0, 0, 2, 2970, 1321860, 187430900, 10199069190, 269591166222, 4221404762120, 44876701584360, 355148098691850, 2230178955481730, 11630998385335692, 52097117078470620, 205557074788375310, 728566149746575350, 2355657801908655120, 7034253747275048912, 19594719516430397970

Offset

0,3

Comments

The Hypercube Graph Q4 has 16 vertices and 32 edges.

All terms are even.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Marc Timme, Frank van Bussel, Denny Fliegner, and Sebastian Stolzenberg, Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions, New Journal of Physics, Volume 11, February 2009.

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 (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Formula

a(n) = n^16 -32*n^15 + ... (see Maple program).

Maple

a:= n-> n^16 -32*n^15 +496*n^14 -4936*n^13 +35264*n^12 -191600*n^11 +818036*n^10 -2794896*n^9 +7701952*n^8 -17100952*n^7 +30276984*n^6 -41821924*n^5 +43389646*n^4 -31680240*n^3 +14412776*n^2 -3040575*n:
seq(a(n), n=0..20);

Mathematica

A158348[n_] := (n - 1)*n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*(n*((n - 31)*n + 465) - 4471) + 30793) - 160807) + 657229) - 2137667) + 5564285) - 11536667) + 18740317) - 23081607) + 20308039) - 11372201) + 3040575);
Array[A158348, 20, 0] (* Paolo Xausa, May 11 2026 *)

Crossrefs

Cf. A140986, A380589.

Column k=4 of A342128.

Sequence in context: A078457 A128148 A308575 * A158904 A358177 A175080

Adjacent sequences: A158345 A158346 A158347 * A158349 A158350 A158351

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 16 2009

Status

approved