OFFSET
0,2
COMMENTS
On a 2n X (n^2 - n + 1) X n^2 cuboid (with n >= 3) there are six pairs of points with the maximum surface distance between them: the four pairs of opposite corners and the opposite pairs of points on the smallest faces 1 in from the midpoints of the shortest edges; this maximum surface distance is sqrt(a(n)).
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
FORMULA
G.f.: (1+5*x+25*x^2+15*x^3+2*x^4)/(1-5*x+10*x^2-10*x^3+5*x^4-x^5). - Colin Barker, Jan 01 2012
MATHEMATICA
Table[2n^4+2n^3+3n^2+2n+1, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 65, 250, 697}, 40] (* Harvey P. Dale, Dec 17 2017 *)
PROG
(PARI) for (n = 0, 500, write("b058920.txt", n, " ", 2*n^4 + 2*n^3 + 3*n^2 + 2*n + 1); ) \\ Harry J. Smith, Jun 24 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jan 11 2001
STATUS
approved