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A320281 Terms that are on the positive x-axis of the square spiral built with 2*k, 2*k+1, 2*k+1 for k >= 0.

%I A320281 #21 Nov 13 2023 04:52:21
%S A320281 0,1,7,18,35,57,84,117,155,198,247,301,360,425,495,570,651,737,828,
%T A320281 925,1027,1134,1247,1365,1488,1617,1751,1890,2035,2185,2340,2501,2667,
%U A320281 2838,3015,3197,3384,3577,3775,3978
%N A320281 Terms that are on the positive x-axis of the square spiral built with 2*k, 2*k+1, 2*k+1 for k >= 0.
%C A320281 Resulting spiral:
%C A320281       28--29--29--30--31--31--32
%C A320281        |
%C A320281       27  13--14--15--15--16--17
%C A320281        |   |                   |
%C A320281       27  13   4---5---5---6  17
%C A320281        |   |   |           |   |
%C A320281       26  12   3   0---1   7  18
%C A320281        |   |   |       |   |   |
%C A320281       25  11   3---2---1   7  19
%C A320281        |   |               |   |
%C A320281       25  11--10---9---9---8  19
%C A320281        |                       |
%C A320281       24--23--23--22--21--21--20
%C A320281 .
%C A320281 a(n) mod 9 is of period 27. a(n) mod 10 is of period 30.
%C A320281 The NE diagonal starting at 1 is A301696. - _Klaus Purath_, May 15 2021
%H A320281 Colin Barker, <a href="/A320281/b320281.txt">Table of n, a(n) for n = 0..1000</a>
%H A320281 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A320281 a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5), a(0)=0, a(1)=1, a(2)=7, a(3)=18, a(4)=35.
%F A320281 a(n+2) - 2*a(n-1) + a(n) = period 3: repeat [5, 5, 6].
%F A320281 a(-n) = 0, 5, 15, 30, 51, 77, 108, 145, ... is the sequence of the terms on the positive y-axis.
%F A320281 G.f.: x*(1 + 5*x + 5*x^2 + 5*x^3) / ((1 - x)^3*(1 + x + x^2)). - _Colin Barker_, Oct 09 2018
%t A320281 LinearRecurrence[{2,-1,1,-2,1},{0,1,7,18,35},100] (* _Paolo Xausa_, Nov 13 2023 *)
%o A320281 (PARI) concat(0, Vec(x*(1 + 5*x + 5*x^2 + 5*x^3) / ((1 - x)^3*(1 + x + x^2)) + O(x^50))) \\ _Colin Barker_, Oct 09 2018
%Y A320281 Cf. A000969.
%K A320281 nonn,easy
%O A320281 0,3
%A A320281 _Paul Curtz_, Oct 09 2018