A058920 a(n) = 2*n^4 + 2*n^3 + 3*n^2 + 2*n + 1.

1, 10, 65, 250, 697, 1586, 3145, 5650, 9425, 14842, 22321, 32330, 45385, 62050, 82937, 108706, 140065, 177770, 222625, 275482, 337241, 408850, 491305, 585650, 692977, 814426, 951185, 1104490, 1275625, 1465922, 1676761, 1909570, 2165825

Offset: 0

Author

Henry Bottomley, Jan 11 2001

Keywords

• nonn
• easy

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
• Source
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

For n >= 2 the sequence is a subsequence of A007692.

Programs

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 *)

PARI

a(n) = 2*n^4 + 2*n^3 + 3*n^2 + 2*n + 1 \\ Harry J. Smith, Jun 24 2009

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