OFFSET
0,5
COMMENTS
The 4-dimensional cross-polytope is sometimes called the 16-cell. It is one of the six convex regular 4-polytopes.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Chromatic Polynomial
Wikipedia, Cross-polytope
Wikipedia, TurĂ¡n graph
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = n*(n - 1)*(n - 2)*(n - 3)*(465 - 392n + 125n^2 - 18n^3 + n^4).
a(n) = -2790n + 7467n^2 - 7852n^3 + 4300n^4 - 1346n^5 + 244n^6 - 24n^7 + n^8.
From Colin Barker, Apr 22 2020: (Start)
G.f.: 24*x^4*(1 + 16*x + 126*x^2 + 536*x^3 + 1001*x^4) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
(End)
PROG
(PARI) concat([0, 0, 0, 0], Vec(24*x^4*(1 + 16*x + 126*x^2 + 536*x^3 + 1001*x^4) / (1 - x)^9 + O(x^30))) \\ Colin Barker, Apr 22 2020
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Peter Kagey, Apr 21 2020
STATUS
approved