A058919 a(n) = n^4/2 - n^3 + 3n^2/2 - n + 1.

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

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) = A002522(n)*A002522(n-1)/2, with A002522(-1)=2. - Bruno Berselli, Nov 11 2014

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

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) { 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.

Cf. A002522, A080827.

Sequence in context: A250555 A147122 A051229 * A018212 A181477 A147274

Adjacent sequences: A058916 A058917 A058918 * A058920 A058921 A058922

Keyword

nonn,easy

Author

Henry Bottomley, Jan 11 2001

Status

approved