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%I #34 Sep 08 2022 08:46:22
%S -2,3,20,55,114,203,328,495,710,979,1308,1703,2170,2715,3344,4063,
%T 4878,5795,6820,7959,9218,10603,12120,13775,15574,17523,19628,21895,
%U 24330,26939,29728,32703,35870,39235,42804,46583,50578,54795,59240,63919,68838,74003,79420,85095
%N a(n) = (n + 2)*(n^2 + n - 1).
%C First differences are in A004538.
%C a(n) is divisible by 11 for n = 3, 7, 9, 14, 18, 20, 25, 29, 31, 36, 40, ... with formula (1/3)*(11*m + (1 + (m mod 3))*(-1)^((m-1) mod 3) + 8), m >= 0.
%H Colin Barker, <a href="/A318765/b318765.txt">Table of n, a(n) for n = 0..1000</a>
%H Bruno Berselli, <a href="/A318765/a318765_1.jpg">Table of similar sequences</a> (row k=3, m>1).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F O.g.f.: (-2 + 11*x - 4*x^2 + x^3)/(1 - x)^4.
%F E.g.f.: (-2 + 5*x + 6*x^2 + x^3)*exp(x).
%F a(n) = -A033445(-n-1).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 5. - _Wesley Ivan Hurt_, Dec 18 2020
%p seq((n+2)*(n^2+n-1),n=0..43); # _Paolo P. Lava_, Sep 04 2018
%t Table[(n + 2) (n^2 + n - 1), {n, 0, 50}]
%o (PARI) vector(50, n, n--; (n+2)*(n^2+n-1))
%o (Sage) [(n+2)*(n^2+n-1) for n in (0..50)]
%o (Maxima) makelist((n+2)*(n^2+n-1), n, 0, 50);
%o (GAP) List([0..50], n -> (n+2)*(n^2+n-1));
%o (Magma) [(n+2)*(n^2+n-1): n in [0..50]];
%o (Python) [(n+2)*(n**2+n-1) for n in range(50)]
%o (Julia) [(n+2)*(n^2+n-1) for n in 0:50] |> println
%Y Cf. A004538.
%Y Subsequence of A047216.
%Y Similar sequences (see Table in Links section): A011379, A027444, A033445, A034262, A045991, A069778.
%K sign,easy
%O 0,1
%A _Bruno Berselli_, Sep 04 2018
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