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A139593 A139276(n) followed by A139272(n+1).

%I A139593 #22 May 04 2021 01:10:18
%S A139593 0,3,11,22,38,57,81,108,140,175,215,258,306,357,413,472,536,603,675,
%T A139593 750,830,913,1001,1092,1188,1287,1391,1498,1610,1725,1845,1968,2096,
%U A139593 2227,2363,2502,2646,2793,2945,3100,3260,3423,3591,3762
%N A139593 A139276(n) followed by A139272(n+1).
%C A139593 Sequence found by reading the line from 0, in the direction 0, 3, ... and the same line from 0, in the direction 0, 11, ..., in the square spiral whose vertices are the triangular numbers A000217.
%C A139593 A139593 appears (both numerically and via back of an envelope algebra, but not a publishable proof) to be the cumulative sum of A047470. - _Markus J. Q. Roberts_, Jul 12 2009
%H A139593 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A139593 Array read by rows: row n gives 8*n^2 + 3n, 8*(n+1)^2 - 5(n+1).
%F A139593 From _Colin Barker_, Sep 15 2013: (Start)
%F A139593 a(n) = (-1 + (-1)^n + 6*n + 8*n^2)/4.
%F A139593 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A139593 G.f.: -x*(5*x+3) / ((x-1)^3*(x+1)). (End)
%e A139593 Array begins:
%e A139593    0,   3;
%e A139593   11,  22;
%e A139593   38,  57;
%e A139593   81, 108;
%t A139593 LinearRecurrence[{2,0,-2,1},{0,3,11,22},50] (* _Harvey P. Dale_, Feb 09 2019 *)
%Y A139593 Cf. A000217, A046092, A139272, A139276, A077221, A139591, A139592, A139594, A139595, A139596, A139597, A139598, A047470.
%K A139593 easy,nonn
%O A139593 0,2
%A A139593 _Omar E. Pol_, May 03 2008
%E A139593 Edited by _Omar E. Pol_, Jul 13 2009