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%I #29 Feb 25 2023 18:07:44
%S 1,18,59,124,213,326,463,624,809,1018,1251,1508,1789,2094,2423,2776,
%T 3153,3554,3979,4428,4901,5398,5919,6464,7033,7626,8243,8884,9549,
%U 10238,10951,11688,12449,13234,14043,14876,15733,16614,17519,18448,19401,20378,21379,22404,23453,24526,25623
%N The 180-degree spoke (or ray) of a hexagonal spiral of Ulam.
%H Colin Barker, <a href="/A244806/b244806.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 - 19*n + 8.
%F See A056105 example section for its formula.
%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 + 15*x + 8*x^2) / (1 - x)^3.
%F (End)
%e See A056105 example section for its diagram.
%p A244806:=n->12*n^2 - 19*n + 8: seq(A244806(n), n=1..50); # _Wesley Ivan Hurt_, Jul 06 2014
%t f[n_] := 12n^2 - 19n + 8; Array[f, 47]
%o (PARI) vector(50, n, 12*n^2 - 19*n + 8) \\ _Michel Marcus_, Jul 06 2014
%o (PARI) Vec(x*(1 + 15*x + 8*x^2) / (1 - x)^3 + O(x^50)) \\ _Colin Barker_, Dec 12 2016
%o (Magma) [12*n^2 - 19*n + 8 : n in [1..50]]; // _Wesley Ivan Hurt_, Jul 06 2014
%Y Cf. A056105, A244802, A056106, A244803, A056107, A244804, A056108, A244805, A056109, A003215, A033577.
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Jul 06 2014
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