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A054398
Define a sequence of 2^n X 2^n squares as follows: S_0 = [1], S_1 = [1,2; 3,4]; S_2 = [1,2,5,6; 3,4,7,8; 9,10,13,14; 11,12,15,16], etc.; sequence gives triangular array whose n-th row gives differences between successive columns of n-th square.
0
1, 1, 3, 1, 1, 3, 1, 11, 1, 3, 1, 1, 3, 1, 11, 1, 3, 1, 43, 1, 3, 1, 11, 1, 3, 1, 1, 3, 1, 11, 1, 3, 1, 43, 1, 3, 1, 11, 1, 3, 1, 171, 1, 3, 1, 11, 1, 3, 1, 43, 1, 3, 1, 11, 1, 3, 1, 1, 3, 1, 11, 1, 3, 1, 43, 1, 3, 1, 11, 1, 3, 1, 171, 1, 3, 1, 11, 1, 3, 1, 43, 1, 3, 1, 11, 1, 3, 1, 683, 1, 3, 1, 11
OFFSET
1,3
EXAMPLE
Triangle begins:
1;
1,3,1;
1,3,1,11,1,3,1;
...
MATHEMATICA
S[0] = {{1}}; S[n_] := S[n] = ArrayFlatten[{{S[n-1], S[n-1] + S[n-1][[-1, -1]]}, {S[n-1] + 2 S[n-1][[-1, -1]], S[n-1] + 3 S[n-1][[-1, -1]]}}];
row[n_] := S[n][[1]] // Differences;
Array[row, 6] // Flatten
(* Second program (without matrices): *)
ro[0] = {1}; ro[n_] := Join[ro[n-1], {(2^(2n+1)+1)/3}, ro[n-1]];
Array[ro, 6, 0] // Flatten (* Jean-François Alcover, Sep 05 2017 *)
CROSSREFS
Sequence in context: A375286 A010274 A137728 * A093415 A233508 A106749
KEYWORD
nonn,tabf,easy,nice
AUTHOR
Tidjani Negadi (t-negadi(AT)usa.net), May 21 2000
EXTENSIONS
More terms from Naohiro Nomoto, Sep 12 2001
STATUS
approved