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 A236630 #30 May 12 2024 11:43:07
%S A236630 1,4,9,8,16,15,25,21,36,32,33,49,40,41,64,55,56,81,65,69,100,84,88,87,
%T A236630 121,96,100,99,144,119,128,127,169,133,142,141,196,160,169,165,225,
%U A236630 176,192,188,189,256,207,223,219,220,289,225,241,237,238
%N A236630 Irregular triangle T(n,k) of alternating sums of squares of entries in the rows in the triangle of A235791, read by rows.
%C A236630 The original name was: Number of "ON" cells at n-th stage in a cellular automaton (or pseudo cellular automaton) related to sigma (see Comments for precise definition).
%H A236630 Michael De Vlieger, <a href="/A236630/b236630.txt">Table of n, a(n) for n = 1..10075</a> (rows n = 1..500, flattened)
%H A236630 Hartmut F. W. Hoft, <a href="/A236630/a236630.pdf">Proof that right border of triangle is A024916</a>
%F A236630 From _Hartmut F. W. Hoft_, Apr 30 2024: (Start)
%F A236630 T(n, k) = Sum_{j = 1 .. k} (-1)^(j + 1) * S(n, j)^2, n >= 0, 1 <= k <= A003056(n), where S(n, j) is the j-th entry in the n-th row of the triangle of A235791.
%F A236630 T(n, k) = Sum_{j = 1 .. k} (-1)^(j+1) * S(n, j), n >= 0, 1 <= k <= A003056(n), where S(n, j) is the j-th entry in the n-th row of the triangle of A236104. (End)
%e A236630 Triangle begins:
%e A236630 1;
%e A236630 4;
%e A236630 9, 8;
%e A236630 16, 15;
%e A236630 25, 21;
%e A236630 36, 32, 33;
%e A236630 49, 40, 41;
%e A236630 64, 55, 56;
%e A236630 81, 65, 69;
%e A236630 100, 84, 88, 87;
%e A236630 121, 96, 100, 99;
%e A236630 144, 119, 128, 127;
%e A236630 169, 133, 142, 141;
%e A236630 196, 160, 169, 165;
%e A236630 225, 176, 192, 188, 189;
%e A236630 256, 207, 223, 219, 220;
%e A236630 289, 225, 241, 237, 238;
%e A236630 ...
%e A236630 From _Omar E. Pol_, Apr 20 2024: (Start)
%e A236630 Illustration of the 6th row as the area of a polygon (or the number of cells) in the fourth quadrant:
%e A236630 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A236630 . | | | | | |
%e A236630 . | | | | | |
%e A236630 . | | | | | |
%e A236630 . | | | _ _| | _|
%e A236630 . | | | | | _|
%e A236630 . |_ _ _ _ _ _| |_ _ _ _| |_ _ _ _|
%e A236630 .
%e A236630 . 36 36 - 4 = 32 36 - 4 + 1 = 33
%e A236630 .
%e A236630 (End)
%t A236630 Map[Accumulate, Table[(-2 Boole[EvenQ[k]] + 1)*Ceiling[(n + 1)/k - (k + 1)/2]^2, {n, 20}, {k, Floor[(Sqrt[8*n + 1] - 1)/2]}]] // Flatten (* _Michael De Vlieger_, Apr 30 2024, after _Hartmut F. W. Hoft_ at A235791 *)
%Y A236630 Row n has length A003056(n).
%Y A236630 The first element of column k is in row A000217(k).
%Y A236630 Column 1 gives the positive terms of A000290.
%Y A236630 Right border gives A024916.
%Y A236630 Row n is the alternating sum of entries in row n of A236104.
%Y A236630 Cf. A003056, A000203, A004125, A026914, A071561, A196020, A235791, A236631, A237048, A237591, A237593, A237270, A249223, A264116, A280851.
%K A236630 nonn,tabf
%O A236630 1,2
%A A236630 _Omar E. Pol_, Jan 29 2014
%E A236630 New name from _Hartmut F. W. Hoft_, Apr 27 2024
%E A236630 0 removed, offset changed and minor edits from _Omar E. Pol_, Apr 28 2024