login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A342075 Number of n-colorings of the vertices of the 7-dimensional cross polytope such that no two adjacent vertices have the same color. 4
0, 0, 0, 0, 0, 0, 0, 5040, 322560, 10342080, 216518400, 3261535200, 37026823680, 325474269120, 2264594492160, 12789814237200, 60389186457600, 245221330273920, 877374833287680, 2821277454690240, 8284633867238400, 22503569636419200, 57135310310453760 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
FORMULA
a(n) = -3597143040*n + 11590795728*n^2 - 15837356724*n^3 + 12355698460*n^4 - 6212542175*n^5 + 2144307578*n^6 - 526197678*n^7 + 93450369*n^8 - 12064836*n^9 + 1122618*n^10 - 73423*n^11 + 3206*n^12 - 84*n^13 + n^14.
a(n) = (n - 6)*(n - 5)*(n - 4)*(n - 3)*(n - 2)*(n - 1)*n*(n^7 - 63 n^6 + 1708 n^5 - 25795 n^4 + 234094 n^3 - 1275281 n^2 + 3858049 n - 4996032).
a(n) = Sum_{i=1..14} A334279(7,i)*n^i.
From Chai Wah Wu, Jan 19 2024: (Start)
a(n) = 15*a(n-1) - 105*a(n-2) + 455*a(n-3) - 1365*a(n-4) + 3003*a(n-5) - 5005*a(n-6) + 6435*a(n-7) - 6435*a(n-8) + 5005*a(n-9) - 3003*a(n-10) + 1365*a(n-11) - 455*a(n-12) + 105*a(n-13) - 15*a(n-14) + a(n-15) for n > 14.
G.f.: x^7*(-52370755920*x^7 - 27190754640*x^6 - 6557740560*x^5 - 959792400*x^4 - 92962800*x^3 - 6032880*x^2 - 246960*x - 5040)/(x - 1)^15. (End)
MATHEMATICA
p = ChromaticPolynomial[CompleteGraph[Table[2, 7]], x];
Table[p /. x -> n, {n, 0, 50}]
CROSSREFS
Analogous for k-dimensional cross polytope: A091940 (k=2), A115400 (k=3), A334281 (k=4), A342073 (k=5), A342074 (k=6).
Sequence in context: A258419 A355023 A179062 * A055362 A246195 A246615
KEYWORD
nonn
AUTHOR
Peter Kagey, Feb 27 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 19 17:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)