This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A121164 #8 Feb 13 2022 23:36:10 %S A121164 -3,-8,-5,-15,-16,-7,-24,-33,-24,-9,-35,-56,-51,-32,-11,-48,-85,-88, %T A121164 -69,-40,-13,-63,-120,-135,-120,-87,-48,-15,-80,-161,-192,-185,-152, %U A121164 -105,-56,-17,-99,-208,-259,-264,-235,-184,-123,-19,-120,-261,-336,-357,-336,-285,-216,-141 %N A121164 Triangle, real terms extracted from squares of paired terms in arithmetic sequences. %C A121164 Left border (-3, -8, -15, -24, ...) unsigned = A013648. Next column (-5, -16, -33, ...) unsigned = A045944. %F A121164 Form an array of the arithmetic sequences: (1, 2, 3, ...); (1, 3, 5, ...); (1, 4, 7, ...); and consider each pair as a complex term; e.g., (1 + 2i), (2 + 3i), then square each complex term and extract the real integer. Antidiagonals become rows of the triangle. %e A121164 Array of the extracted real terms: %e A121164 -3, -5, -7, -9, ... %e A121164 -8, -16, -24, -32, ... %e A121164 -15, -33, -51, -69, ... %e A121164 -24, -56, -88, -120, ... %e A121164 ... %e A121164 Taking antidiagonals we get the triangle: %e A121164 -3; %e A121164 -8, -5; %e A121164 -15, -16, -7; %e A121164 -24, -33, -24, -9; %e A121164 -35, -56, -51, -32, -11; %e A121164 -48, -85, -88, -69, -40, -13; %e A121164 ... %e A121164 (3,2) = -16 since (taken from the arithmetic sequence 1, 3, 5, ...), (3 + 5i)^2 = (-16 + 30i). %Y A121164 Cf. A013648, A045944. %K A121164 sign,tabl %O A121164 1,1 %A A121164 _Gary W. Adamson_, Aug 13 2006