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%I #17 Sep 08 2022 08:46:08
%S 1,12,47,106,189,296,427,582,761,964,1191,1442,1717,2016,2339,2686,
%T 3057,3452,3871,4314,4781,5272,5787,6326,6889,7476,8087,8722,9381,
%U 10064,10771,11502,12257,13036,13839,14666,15517,16392,17291,18214,19161,20132,21127,22146,23189,24256,25347
%N The 360 degree spoke (or ray) of a hexagonal spiral of Ulam.
%H Colin Barker, <a href="/A244803/b244803.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 See A056105 example section for a 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 + 2*x)*((1 + 7*x) / (1 - x)^3).
%F (End)
%e See A056105 example section for a diagram.
%p A244803:=n->12*n^2-25*n+14: seq(A244803(n), n=1..50); # _Wesley Ivan Hurt_, Jul 06 2014
%t f[n_] := 12n^2 - 25n + 14; Array[f, 47]
%o (PARI) vector(50, n, 12*n^2 - 25*n + 14) \\ _Michel Marcus_, Jul 06 2014
%o (PARI) Vec(x*(1 + 2*x)*((1 + 7*x) / (1 - x)^3) + O(x^50)) \\ _Colin Barker_, Dec 12 2016
%o (Magma) [12*n^2-25*n+14 : n in [1..50]]; // _Wesley Ivan Hurt_, Jul 06 2014
%Y Cf. A056105, A244802, A056106, A056107, A244804, A056108, A244805, A056109, A244806, A003215, A033577.
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Jul 06 2014
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