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A106344
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Triangle read by rows: T(n,k) = binomial(k,n-k) mod 2.
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15
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1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1
(list;
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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A skew version of Sierpinski’s triangle A047999. - Johannes W. Meijer, Jun 05 2011
Row sums are A002487(n+1). Diagonal sums are A106345. Inverse is A106346.
Triangle formed by reading T triangle mod 2 with T := A026729, A062110, A084938, A099093, A106344, A109466, A110517, A112883, A130167. - Philippe Deléham, Dec 18 2008
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LINKS
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G. C. Greubel, Rows n = 0..50, flattened
Thomas Baruchel, Flattening Karatsuba's Recursion Tree into a Single Summation, SN Computer Science (2020) Vol. 1, Article No. 48.
George Beck and Karl Dilcher, A Matrix Related to Stern Polynomials and the Prouhet-Thue-Morse Sequence, arXiv:2106.10400 [math.CO], 2021. See (1.6) p. 2.
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EXAMPLE
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Triangle begins
1;
0, 1;
0, 1, 1;
0, 0, 0, 1;
0, 0, 1, 1, 1;
0, 0, 0, 1, 0, 1;
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MAPLE
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seq(seq(`mod`(binomial(k, n-k), 2), k = 0..n), n = 0..15); # G. C. Greubel, Feb 07 2020
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MATHEMATICA
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Table[Mod[Binomial[k, n-k], 2], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Apr 18 2017 *)
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PROG
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(PARI) T(n, k) = binomial(k, n-k)%2;
for(n=0, 15, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Feb 07 2020
(Magma) [ Binomial(k, n-k) mod 2: k in [0..n], n in [0..15]]; // G. C. Greubel, Feb 07 2020
(Sage) [[ mod(binomial(k, n-k), 2) for k in (0..n)] for n in (0..15)] # G. C. Greubel, Feb 07 2020
(GAP) Flat(List([0..15], n-> List([0..n], k-> (Binomial(k, n-k) mod 2) ))); # G. C. Greubel, Feb 07 2020
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CROSSREFS
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Cf. A047999, A002487.
Cf. A106345 (diagonal sums), A106346 (inverse).
Cf. A026729, A062110, A084938, A099093, A106344, A109466, A110517, A112883, A130167.
Sequence in context: A321016 A077051 A115955 * A106346 A296212 A189921
Adjacent sequences: A106341 A106342 A106343 * A106345 A106346 A106347
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry, Apr 29 2005
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STATUS
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approved
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