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A106344 Triangle read by rows: T(n,k) = binomial(k,n-k) mod 2.

%I A106344 #26 May 21 2022 08:31:24
%S A106344 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,
%T A106344 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,
%U A106344 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
%N A106344 Triangle read by rows: T(n,k) = binomial(k,n-k) mod 2.
%C A106344 A skew version of Sierpinski’s triangle A047999. - _Johannes W. Meijer_, Jun 05 2011
%C A106344 Row sums are A002487(n+1). Diagonal sums are A106345. Inverse is A106346.
%C A106344 Triangle formed by reading T triangle mod 2 with T := A026729, A062110, A084938, A099093, A106344, A109466, A110517, A112883, A130167. - _Philippe Deléham_, Dec 18 2008
%H A106344 G. C. Greubel, <a href="/A106344/b106344.txt">Rows n = 0..50, flattened</a>
%H A106344 Thomas Baruchel, <a href="https://doi.org/10.1007/s42979-019-0049-1">Flattening Karatsuba's Recursion Tree into a Single Summation</a>, SN Computer Science (2020) Vol. 1, Article No. 48.
%H A106344 George Beck and Karl Dilcher, <a href="https://arxiv.org/abs/2106.10400">A Matrix Related to Stern Polynomials and the Prouhet-Thue-Morse Sequence</a>, arXiv:2106.10400 [math.CO], 2021. See (1.6) p. 2.
%e A106344 Triangle begins
%e A106344   1;
%e A106344   0, 1;
%e A106344   0, 1, 1;
%e A106344   0, 0, 0, 1;
%e A106344   0, 0, 1, 1, 1;
%e A106344   0, 0, 0, 1, 0, 1;
%p A106344 seq(seq(`mod`(binomial(k, n-k), 2), k = 0..n), n = 0..15); # _G. C. Greubel_, Feb 07 2020
%t A106344 Table[Mod[Binomial[k, n-k], 2], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Apr 18 2017 *)
%o A106344 (PARI) T(n,k) = binomial(k,n-k)%2;
%o A106344 for(n=0,15, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Feb 07 2020
%o A106344 (Magma) [ Binomial(k,n-k) mod 2: k in [0..n], n in [0..15]]; // _G. C. Greubel_, Feb 07 2020
%o A106344 (Sage) [[ mod(binomial(k,n-k), 2) for k in (0..n)] for n in (0..15)] # _G. C. Greubel_, Feb 07 2020
%o A106344 (GAP) Flat(List([0..15], n-> List([0..n], k-> (Binomial(k,n-k) mod 2) ))); # _G. C. Greubel_, Feb 07 2020
%Y A106344 Cf. A047999, A002487.
%Y A106344 Cf. A106345 (diagonal sums), A106346 (inverse).
%Y A106344 Cf. A026729, A062110, A084938, A099093, A106344, A109466, A110517, A112883, A130167.
%K A106344 easy,nonn,tabl
%O A106344 0,1
%A A106344 _Paul Barry_, Apr 29 2005