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A322465 Numbers on the 0-9-10-line in a spiral on an equilateral triangular lattice.

%I A322465 #33 Feb 14 2019 14:22:47
%S A322465 0,9,10,31,32,65,66,111,112,169,170,239,240,321,322,415,416,521,522,
%T A322465 639,640,769,770,911,912,1065,1066,1231,1232,1409,1410,1599,1600,1801,
%U A322465 1802,2015,2016,2241,2242,2479,2480,2729,2730,2991,2992,3265,3266,3551,3552
%N A322465 Numbers on the 0-9-10-line in a spiral on an equilateral triangular lattice.
%C A322465 Sequence found by reading the line from 0, in the direction 0, 9, 10, ... in the triangle spiral.
%H A322465 Colin Barker, <a href="/A322465/b322465.txt">Table of n, a(n) for n = 0..1000</a>
%H A322465 Hans G. Oberlack, <a href="/A322465/a322465.png">Triangle spiral line 0-9-10</a>
%H A322465 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A322465 For even n: a(n) = n*((3/2)*n+2).
%F A322465 For odd n: a(n) = a(n+1)-1 = (n+1)*((3/2)*(n+1)+2)-1.
%F A322465 From _Colin Barker_, Dec 18 2018: (Start)
%F A322465 G.f.: x*(9 + x + 3*x^2 - x^3) / ((1 - x)^3*(1 + x)^2).
%F A322465 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.
%F A322465 (End)
%p A322465 a:= n-> `if`(n::even, n*((3/2)*n+2), (n+1)*((3/2)*(n+1)+2)-1): seq(a(n), n=0..50); # _Muniru A Asiru_, Dec 20 2018
%o A322465 (PARI) concat(0, Vec(x*(9 + x + 3*x^2 - x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ _Colin Barker_, Dec 18 2018
%Y A322465 Bisection (even part) gives A202804.
%K A322465 nonn,easy
%O A322465 0,2
%A A322465 _Hans G. Oberlack_, Dec 09 2018