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%I #29 Apr 23 2023 07:25:41
%S 0,10,40,102,208,370,600,910,1312,1818,2440,3190,4080,5122,6328,7710,
%T 9280,11050,13032,15238,17680,20370,23320,26542,30048,33850,37960,
%U 42390,47152,52258,57720,63550,69760,76362,83368,90790,98640,106930,115672,124878,134560
%N a(n) = 2*(n-1)*(n^2 + 1).
%C 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
%D T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
%H Vincenzo Librandi, <a href="/A071233/b071233.txt">Table of n, a(n) for n = 1..2000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F G.f.: 2*x*(5+x^2)/(1 - x)^4 - _Harvey P. Dale_, Jun 27 2021
%F E.g.f.: 2*exp(x)*x*(5 + 5*x + x^2). - _Stefano Spezia_, Apr 22 2023
%e From _Wesley Ivan Hurt_, May 13 2021: (Start)
%e Given the 4 X 4 square array below,
%e [ 1 2 3 4 ]
%e [ 5 6 7 8 ]
%e [ 9 10 11 12 ]
%e [ 13 14 15 16 ]
%e 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)
%t 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 *)
%o (Magma) [2*(n-1)*(n^2+1): n in [1..50]]; // _Vincenzo Librandi_, Jun 14 2011
%Y Twice A062158.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jun 11 2002
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