A071233 a(n) = 2*(n-1)*(n^2 + 1).

0, 10, 40, 102, 208, 370, 600, 910, 1312, 1818, 2440, 3190, 4080, 5122, 6328, 7710, 9280, 11050, 13032, 15238, 17680, 20370, 23320, 26542, 30048, 33850, 37960, 42390, 47152, 52258, 57720, 63550, 69760, 76362, 83368, 90790, 98640, 106930, 115672, 124878, 134560

Offset: 1

Author

N. J. A. Sloane, Jun 11 2002

Keywords

• nonn
• easy

Comments

For n > 1, a(n) is the sum of the numbers appearing along the outside border of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - Wesley Ivan Hurt, May 13 2021

Examples

			From _Wesley Ivan Hurt_, May 13 2021: (Start)
Given the 4 X 4 square array below,
  [  1   2   3   4 ]
  [  5   6   7   8 ]
  [  9  10  11  12 ]
  [ 13  14  15  16 ]
the sum of the elements along the outside border is 1+2+3+4+8+12+16+15+14+13+9+5 = 102. Thus a(4) = 102. (End)
		

References

• T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A005893, A062158.

Programs

Magma

[2*(n-1)*(n^2+1): n in [1..50]]; // Vincenzo Librandi, Jun 14 2011

Mathematica

Table[2(n-1)(n^2+1),{n,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,10,40,102},50] (* Harvey P. Dale, Jun 27 2021 *)

SageMath

def A071233(n): return 2*(n-1)*(n^2+1)
[A071233(n) for n in range(1,51)] # G. C. Greubel, Aug 05 2024

Formula

a(n) = 2*A062158(n).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: 2*x*(5+x^2)/(1 - x)^4 - Harvey P. Dale, Jun 27 2021

E.g.f.: 2*exp(x)*x*(5 + 5*x + x^2). - Stefano Spezia, Apr 22 2023

a(n) = (n-1)*A005893(n). - G. C. Greubel, Aug 05 2024