OFFSET
0,3
COMMENTS
On an n X (n - 1)(n - 2)/2 X n(n - 1)/2 cuboid with n >= 5, the two points at greatest surface distance from a corner are the opposite corner and the point 1 in from each of the two edges on a smallest face which meet at the opposite corner; this greatest surface distance is sqrt(a(n)).
Subsequence of A080827, see formula. - David James Sycamore, Jul 31 2018
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..500
Henry Bottomley, Source
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: (1 - 4*x + 10*x^2 + 5*x^4)/(1 - x)^5. - Colin Barker, Jan 01 2012
a(n) = A080827(n^2-n+1). - David James Sycamore, Jul 31 2018
E.g.f.: exp(x)*(2 + 4*x^2 + 4*x^3 + x^4)/2. - Stefano Spezia, Oct 08 2022
For n>1, a(n) = A000217(n-1)^2 + (A000217(n-1)+1)^2 = (A000217(n)-1)^2 + (A000217(n-2)-1)^2. - Charlie Marion, Feb 08 2024
MAPLE
A058919:=n->n^4/2 - n^3 + 3*n^2/2 - n + 1; seq(A058919(n), n=0..30); # Wesley Ivan Hurt, May 10 2014
MATHEMATICA
Table[n^4/2 - n^3 + 3 n^2/2 - n + 1, {n, 0, 30}] (* Wesley Ivan Hurt, May 10 2014 *)
PROG
(PARI) a(n) = { (n^4 + 3*n^2)/2 - n^3 - n + 1 } \\ Harry J. Smith, Jun 23 2009
(Magma) [n^4/2 - n^3 + 3*n^2/2 - n + 1: n in [0..30]]; // Wesley Ivan Hurt, May 10 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jan 11 2001
STATUS
approved