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 A262057 Array based on the Stanley sequence S(0), A005836, by antidiagonals. 2
 0, 2, 1, 7, 5, 3, 21, 8, 6, 4, 23, 22, 16, 11, 9, 64, 26, 24, 17, 14, 10, 69, 65, 50, 25, 19, 15, 12, 71, 70, 67, 53, 48, 20, 18, 13, 193, 80, 78, 68, 59, 49, 34, 29, 27, 207, 194, 152, 79, 73, 62, 51, 35, 32, 28, 209, 208, 196, 161, 150, 74, 63, 52, 43, 33, 30 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This array is similar to a dispersion in that the first column is the minimal nonnegative sequence that contains no 3-term arithmetic progression, and each next column is the minimal sequence consisting of the numbers rejected from the previous column that contains no 3-term arithmetic progression. A100480(n) describes which column n is sorted into. The columns of the array form the greedy partition of the nonnegative integers into sequences that contain no 3-term arithmetic progression. - Robert Israel, Feb 03 2016 LINKS Max Barrentine and Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals, flattened; n=1..77 from Max Barrentine) EXAMPLE From the top-left corner, this array starts:    0   2   7  21  23  64    1   5   8  22  26  65    3   6  16  24  50  67    4  11  17  25  53  68    9  14  19  48  59  73   10  15  20  49  62  74 MAPLE M:= 20: # to get the first M antidiagonals for i from 1 to M do B[i]:= {}: F[i]:= {}: od: countdowns:= Vector(M, j->M+1-j): for x from 0 while max(countdowns) > 0 do   for i from 1 do      if not member(x, F[i]) then        F[i]:= F[i] union map(y -> 2*x-y, B[i]);        B[i]:= B[i] union {x};        countdowns[i]:= countdowns[i] - 1;      break     fi   od; od: seq(seq(B[n+1-i][i], i=1..n), n=1..M); # Robert Israel, Feb 03 2016 PROG (MATLAB) function  A = A262057( M, N ) % to get first M antidiagonals using x up to N B = cell(1, M); F = zeros(M, N+1); countdowns = [M:-1:1]; for x=0:N     if max(countdowns) == 0         break     end     for i=1:M         if F(i, x+1) == 0             newforb = 2*x - B{i};             newforb = newforb(newforb <= N & newforb >= 1);             F(i, newforb+1) = 1;             B{i}(end+1) = x;             countdowns(i) = countdowns(i)-1;             break         end     end end if max(countdowns) > 0     [~, jmax] = max(countdowns);     jmax = jmax(1);     error ('Need larger N: B{%d} has only %d elements', jmax, numel(B{jmax})); end A = zeros(1, M*(M+1)/2); k = 0; for n=1:M     for i=1:n         k=k+1;         A(k) = B{n+1-i}(i);     end end end % Robert Israel, Feb 03 2016 CROSSREFS First column is A005836. First row is A265316. Cf. A074940, A100480. Sequence in context: A124821 A104030 A206533 * A082791 A299238 A077230 Adjacent sequences:  A262054 A262055 A262056 * A262058 A262059 A262060 KEYWORD nonn,tabl AUTHOR Max Barrentine, Nov 29 2015 STATUS approved

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Last modified January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)