OFFSET
1,2
COMMENTS
Each member of a chiral pair is a reflection, but not a rotation, of the other. Both the cube and the octahedron have 12 edges.
LINKS
Index entries for linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
FORMULA
a(n) = (n-1) * n^2 * (n+1) * (n^8 + n^6 - 2n^4 + 8) / 48.
a(n) = 74*C(n,2) + 10482*C(n,3) + 303268*C(n,4) + 3440700*C(n,5) + 19842840*C(n,6) + 65867760*C(n,7) + 133580160*C(n,8) + 168399000*C(n,9) + 128898000*C(n,10) + 54885600*C(n,11) + 9979200*C(n,12), where the coefficient of C(n,k) is the number of colorings using exactly k colors.
G.f.: 2 * (37*x^2 + 4871*x^3 + 106130*x^4 + 691514*x^5 + 1692248*x^6 + 1692248*x^7 + 691514*x^8 + 106130*x^9 + 4871*x^10 + 37*x^11) / (1-x)^13.
MATHEMATICA
Table[(n-1)n^2(n+1)(n^8+n^6-2n^4+8)/48, {n, 20}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert A. Russell, Aug 26 2020
STATUS
approved