

A058919


a(n) = n^4/2  n^3 + 3n^2/2  n + 1.


3



1, 1, 5, 25, 85, 221, 481, 925, 1625, 2665, 4141, 6161, 8845, 12325, 16745, 22261, 29041, 37265, 47125, 58825, 72581, 88621, 107185, 128525, 152905, 180601, 211901, 247105, 286525, 330485, 379321, 433381, 493025, 558625, 630565, 709241
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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)).


LINKS



FORMULA

G.f.: (1  4*x + 10*x^2 + 5*x^4)/(1  x)^5.  Colin Barker, Jan 01 2012
E.g.f.: exp(x)*(2 + 4*x^2 + 4*x^3 + x^4)/2.  Stefano Spezia, Oct 08 2022


MAPLE



MATHEMATICA

Table[n^4/2  n^3 + 3 n^2/2  n + 1, {n, 0, 30}] (* Wesley Ivan Hurt, May 10 2014 *)


PROG

(PARI) { for (n = 0, 500, write("b058919.txt", 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

For n >= 4 the sequence is a subsequence of A007692.


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



