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%I #30 Feb 27 2023 03:58:09
%S 1,16,55,118,205,316,451,610,793,1000,1231,1486,1765,2068,2395,2746,
%T 3121,3520,3943,4390,4861,5356,5875,6418,6985,7576,8191,8830,9493,
%U 10180,10891,11626,12385,13168,13975,14806,15661,16540,17443,18370,19321,20296,21295,22318,23365,24436,25531
%N The 240-degree spoke (or ray) of a hexagonal spiral of Ulam.
%C Numbers of the form 1 + k/2 + k^2/3 (associated k are in A008588). - _Bruno Berselli_, Jan 20 2017
%H Colin Barker, <a href="/A244805/b244805.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 12*n^2 - 21*n + 10 (see A056105).
%F From _Colin Barker_, Dec 12 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F G.f.: x*(1 + 13*x + 10*x^2) / (1 - x)^3.
%F (End)
%e See A056105 example section for its diagram.
%p A244805:=n->12*n^2 - 21*n + 10: seq(A244805(n), n=1..50); # _Wesley Ivan Hurt_, Jul 06 2014
%t f[n_] := 12 n^2 - 21 n + 10; Array[f, 47]
%o (PARI) vector(50, n, 12*n^2 - 21*n + 10) \\ _Michel Marcus_, Jul 06 2014
%o (PARI) Vec(x*(1 + 13*x + 10*x^2) / (1 - x)^3 + O(x^50)) \\ _Colin Barker_, Dec 12 2016
%o (Magma) [12*n^2-21*n+10: n in [1..50]]; // _Wesley Ivan Hurt_, Jul 06 2014
%Y Cf. A056105, A244802, A056106, A244803, A056107, A244804, A056108, A056109, A244806, A003215, A033577.
%Y Cf. A281333 (1 + floor(n/2) + floor(n^2/3)).
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Jul 06 2014
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