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A090971
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Sierpiński's triangle, read by rows, starting from 1: T(n,k) = (T(n-1,k) + T(n-1,k-1)) mod 2.
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2
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1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1
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OFFSET
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1,1
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COMMENTS
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Row sums give A038573.
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LINKS
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G. C. Greubel, Rows n = 1..100 of triangle, flattened
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FORMULA
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From Philippe Deléham, Feb 29 2004: (Start)
Triangle A047999(n, k) for n > 0 and k > 0; A047999: Pascal's triangle mod 2.
a(n) = A062534(n-1) mod 2.
T(n-1, k-1) = A074909(n, n-k) mod 2.
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EXAMPLE
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Triangle begins with:
1;
0, 1;
1, 1, 1;
0, 0, 0, 1;
1, 0, 0, 1, 1;
0, 1, 0, 1, 0, 1;
1, 1, 1, 1, 1, 1, 1; ...
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[k==n, 1, Mod[T[n-1, k] + T[n-1, k-1], 2]]]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] (* G. C. Greubel, Feb 03 2019 *)
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PROG
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(PARI) T(n, k)=if(k<0 || k>n, 0, if(n==0, 1, (T(n-1, k)+T(n-1, k-1))%2))
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CROSSREFS
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Cf. A007318.
Sequence in context: A267814 A267272 A181656 * A105594 A091949 A039984
Adjacent sequences: A090968 A090969 A090970 * A090972 A090973 A090974
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KEYWORD
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nonn,tabl
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AUTHOR
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Benoit Cloitre, Feb 28 2004
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STATUS
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approved
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