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.
Table begins: 0, 1,0, 2,0,0, 4,1,0,0, 8,1,0,0,0, 16,4,1,0,0,0, 32,6,1,0,0,0,0,
Triangle starts: 1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 8, 4, 2, 1, 1, 16, 8, 4, 2, 1, 1, 32, 16, 8, 4, 2, 1, 1, 64, 32, 16, 8, 4, 2, 1, 1, 128, 64, 32, 16, 8, 4, 2, 1, 1, 256, 128, 64, 32, 16, 8, 4, 2, 1, 1, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 1, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 1, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, ... - _Joerg Arndt_, May 04 2014 When viewed as a triangular array, row 8 of A023758 is 128 192 224 240 248 252 254 255 so row 8 here is 1 64 32 16 8 4 2 1 From _Mats Granvik_, Jan 19 2009: (Start) Except for the first term the table can also be formatted as: 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 8, 4, 2, 1, 1, 16, 8, 4, 2, 1, 1, ... (End)
a057728 n k = a057728_tabl !! (n-1) !! (k-1) a057728_row n = a057728_tabl !! (n-1) a057728_tabl = iterate (\row -> zipWith (+) (row ++ [0]) ([0] ++ tail row ++ [1])) [1] -- Reinhard Zumkeller, Aug 08 2013
nn=10;Map[Select[#,#>0&]&,CoefficientList[Series[(x-x^2)/(1-2x)/(1-y x),{x,0,nn}],{x,y}]]//Grid (* Geoffrey Critzer, Jan 28 2014 *)
Module[{nn=12,ts},ts=2^Range[0,nn];Table[Join[{1},Reverse[Take[ts,n]]],{n,0,nn}]]//Flatten (* Harvey P. Dale, Jan 15 2022 *)
T(n, k) := if k = 0 then 1 else 2^(n - k - 1)$ create_list(T(n, k), n, 0, 12, k, 0, n - 1); /* Franck Maminirina Ramaharo, Jan 09 2019 */
Last /@ Table[SortBy[Range@ k, And[Total@ IntegerDigits[#, 2], k] &], {k, 67}] (* Michael De Vlieger, Oct 04 2015 *)
cmph(i, j) = if (hammingweight(i) != hammingweight(j), hammingweight(i) - hammingweight(j), i - j);
row(n) = my(v = vector(n+1, k, k-1)); vecsort(v, cmph);
lista(nn) = {for (n=0, nn, my(r = srow(n)); print1(r[#r], ", "););}
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