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A355604 Table T(n, k), n >= 0, k = 0..n, read by rows; row n is obtained by replacing in row n of Pascal's triangle (A007318) runs of k consecutive even numbers by the terms of row k+1 of the present triangle.

%I A355604 #12 Jul 11 2022 20:48:41
%S A355604 1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,5,1,1,5,1,1,1,15,1,15,1,1,1,7,21,35,
%T A355604 35,21,7,1,1,1,1,15,1,15,1,1,1,1,9,1,5,1,1,5,1,9,1,1,1,45,1,1,1,1,1,
%U A355604 45,1,1,1,11,55,165,1,3,3,1,165,55,11,1,1,1,1,1,495,1,1,1,495,1,1,1,1
%N A355604 Table T(n, k), n >= 0, k = 0..n, read by rows; row n is obtained by replacing in row n of Pascal's triangle (A007318) runs of k consecutive even numbers by the terms of row k+1 of the present triangle.
%C A355604 This triangle has fractal features: even terms of Pascal's triangle are clustered as wXwXw subtriangles; these subtriangles are replaced by the first w rows (flipped upside-down) of the present triangle.
%H A355604 Rémy Sigrist, <a href="/A355604/b355604.txt">Table of n, a(n) for n = 0..8384</a> (rows for n = 0..128 flattened)
%H A355604 Rémy Sigrist, <a href="/A355604/a355604.png">Colored representation of the first 2^10 rows</a> (where the hue is function of T(n, k), black pixels correspond to 1's)
%H A355604 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%e A355604 Triangle T(n, k) begins (stars indicate replacements):
%e A355604   n\k|   0    1    2    3    4    5    6    7    8    9   10   11   12
%e A355604   ---+-----------------------------------------------------------------
%e A355604     0|   1
%e A355604     1|   1    1
%e A355604     2|   1    1*   1
%e A355604     3|   1    3    3    1
%e A355604     4|   1    1*   1*   1*   1
%e A355604     5|   1    5    1*   1*   5    1
%e A355604     6|   1    1*  15    1*  15    1*   1
%e A355604     7|   1    7   21   35   35   21    7    1
%e A355604     8|   1    1*   1*  15*   1*  15*   1*   1*   1
%e A355604     9|   1    9    1*   5*   1*   1*   5*   1*   9    1
%e A355604    10|   1    1*  45    1*   1*   1*   1*   1*  45    1*   1
%e A355604    11|   1   11   55  165    1*   3*   3*   1* 165   55   11    1
%e A355604    12|   1    1*   1*   1* 495    1*   1*   1* 495    1*   1*   1*   1
%o A355604 (PARI) row(n) = { my (r=binomial(n)); for (i=1, #r, if (r[i]%2==0, for (w=1, oo, if (r[i+w]%2==1, my (t=row(w-1)); for (j=1, #t, r[i-1+j]=t[j]); i+=w; break)))); return (r) }
%Y A355604 Cf. A007318, A065040, A014421, A143333, A348648.
%K A355604 nonn,look,tabl
%O A355604 0,8
%A A355604 _Rémy Sigrist_, Jul 09 2022