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A100182 Structured tetragonal anti-prism numbers. 2

%I

%S 1,8,28,68,135,236,378,568,813,1120,1496,1948,2483,3108,3830,4656,

%T 5593,6648,7828,9140,10591,12188,13938,15848,17925,20176,22608,25228,

%U 28043,31060,34286,37728,41393,45288,49420,53796,58423,63308,68458,73880,79581,85568,91848,98428,105315,112516

%N Structured tetragonal anti-prism numbers.

%C If offset is changed to 0, this is the number of magic labelings of the 5-node, 8-edge graph formed from a square with both diagonals drawn and a node at the center [Stanley]. - _N. J. A. Sloane_, Jul 07 2014

%H Vincenzo Librandi, <a href="/A100182/b100182.txt">Table of n, a(n) for n = 1..10000</a>

%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = (1/6)*(7*n^3 - 3*n^2 + 2*n). [Corrected by _Luca Colucci_, Mar 01 2011]

%F G.f.: x*(1 + 4*x + 2*x^2)/(1-x)^4. - _Colin Barker_, Jun 08 2012

%F E.g.f.: (6*x +18*x^2 +7*x^3)*exp(x)/6. - _G. C. Greubel_, Nov 08 2018

%F a(n) = binomial(n,3) + n^3. - _Pedro Caceres_, Jul 28 2019

%t Table[(7*n^3 - 3*n^2 + 2*n)/6, {n,1,40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 8, 28, 68}, 40] (* _G. C. Greubel_, Nov 08 2018 *)

%o (MAGMA) [(1/6)*(7*n^3-3*n^2+2*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 18 2011

%o (PARI) vector(40, n, (7*n^3 -3*n^2 +2*n)/6) \\ _G. C. Greubel_, Nov 08 2018

%Y Cf. A100185 - structured anti-prisms; A100145 for more on structured numbers.

%K easy,nonn

%O 1,2

%A James A. Record (james.record(AT)gmail.com), Nov 07 2004

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Last modified April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)