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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..93.

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-Fran├žois Alcover, Sep 05 2017 *)

CROSSREFS

Sequence in context: A122506 A010274 A137728 * A093415 A233508 A106749

Adjacent sequences:  A054395 A054396 A054397 * A054399 A054400 A054401

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

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Last modified August 10 12:39 EDT 2020. Contains 336379 sequences. (Running on oeis4.)