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A027444 a(n) = n^3 + n^2 + n.

%I A027444 #40 Apr 10 2025 10:45:54
%S A027444 0,3,14,39,84,155,258,399,584,819,1110,1463,1884,2379,2954,3615,4368,
%T A027444 5219,6174,7239,8420,9723,11154,12719,14424,16275,18278,20439,22764,
%U A027444 25259,27930,30783,33824,37059,40494,44135,47988,52059,56354,60879,65640,70643,75894
%N A027444 a(n) = n^3 + n^2 + n.
%C A027444 For n>1, a(n) is the volume of a truncated square pyramid with height n and base lengths n+2 and n-1. - _Wesley Ivan Hurt_, Apr 05 2016
%H A027444 Vincenzo Librandi, <a href="/A027444/b027444.txt">Table of n, a(n) for n = 0..1000</a>
%H A027444 D. Applegate, M. LeBrun, and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.
%H A027444 Milan Janjic, <a href="https://old.pmf.unibl.org/wp-content/uploads/2017/10/enumfun.pdf">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A027444 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MagicCircles.html">Magic Circles</a>.
%H A027444 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A027444 O.g.f.: x*(3 + 2*x + x^2)/(1 - x)^4. - _R. J. Mathar_, Feb 04 2008
%F A027444 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - _Wesley Ivan Hurt_, Apr 05 2016
%e A027444 For n = 4, 4^3 + 4^2 + 4 = 64 + 16 + 4 = 84.
%p A027444 A027444:=n->n^3+n^2+n: seq(A027444(n), n=0..100); # _Wesley Ivan Hurt_, Apr 05 2016
%t A027444 Table[n^3 + n^2 + n, {n, 0, 50}] (* _Harvey P. Dale_, Dec 13 2013 *)
%o A027444 (Magma) [n^3 + n^2 + n: n in [0..50]]; // _Vincenzo Librandi_, Jun 09 2011
%Y A027444 Column k=3 of A228275.
%Y A027444 Cf. A270109.
%K A027444 nonn,easy
%O A027444 0,2
%A A027444 _Patrick De Geest_ and Mark Milhet (mm992395(AT)shellus.com)