cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A130047 Left half of Pascal's triangle (A034868) modulo 2.

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%I A130047 #28 Aug 15 2017 11:09:26
%S A130047 1,1,1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,0,
%T A130047 0,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,
%U A130047 1,1,1,1,1,0,0,0,0,0,0
%N A130047 Left half of Pascal's triangle (A034868) modulo 2.
%C A130047 Row sums yield: 1, 1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 4, 8, 1, 2, 2, 4, 2, 4, 4, 8, ...(see A048896).
%H A130047 G. C. Greubel, <a href="/A130047/b130047.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%F A130047 T(n,k) = mod(binomial(n, k), 2), 0 <= k <= floor(n/2). - _G. C. Greubel_, Aug 12 2017
%e A130047 Triangle begins:
%e A130047 1,
%e A130047 1,
%e A130047 1, 0,
%e A130047 1, 1,
%e A130047 1, 0, 0,
%e A130047 1, 1, 0,
%e A130047 1, 0, 1, 0,
%e A130047 1, 1, 1, 1,
%e A130047 1, 0, 0, 0, 0,
%e A130047 1, 1, 0, 0, 0,
%e A130047 1, 0, 1, 0, 0, 0,
%e A130047 1, 1, 1, 1, 0, 0,
%e A130047 1, 0, 0, 0, 1, 0, 0,
%e A130047 1, 1, 0, 0, 1, 1, 0,
%e A130047 1, 0, 1, 0, 1, 0, 1, 0,
%e A130047 1, 1, 1, 1, 1, 1, 1, 1,
%e A130047 1, 0, 0, 0, 0, 0, 0, 0, 0,
%e A130047 ...
%e A130047 Triangle (right aligned) begins:
%e A130047                                   1,
%e A130047                                 1,
%e A130047                               1,  0,
%e A130047                             1,  1,
%e A130047                           1,  0,  0,
%e A130047                         1,  1,  0,
%e A130047                       1,  0,  1,  0,
%e A130047                     1,  1,  1,  1,
%e A130047                   1,  0,  0,  0,  0,
%e A130047                 1,  1,  0,  0,  0,
%e A130047               1,  0,  1,  0,  0,  0,
%e A130047             1,  1,  1,  1,  0,  0,
%e A130047           1,  0,  0,  0,  1,  0,  0,
%e A130047         1,  1,  0,  0,  1,  1,  0,
%e A130047       1,  0,  1,  0,  1,  0,  1,  0,
%e A130047     1,  1,  1,  1,  1,  1,  1,  1,
%e A130047   1,  0,  0,  0,  0,  0,  0,  0,  0,
%e A130047 1,  1,  0,  0,  0,  0,  0,  0,  0,
%e A130047 ...
%p A130047 # From _N. J. A. Sloane_, Mar 22 2015:
%p A130047 for n from 0 to 20 do
%p A130047 lprint(seq(binomial(n,k) mod 2, k=0..floor(n/2))); od:
%p A130047 # For row sums:
%p A130047 f:=n->add(binomial(n,k) mod 2, k=0..floor(n/2));
%p A130047 [seq(f(n),n=0..60)];
%t A130047 Table[Mod[Binomial[n, k], 2], {n, 0, 10}, {k, 0, Floor[n/2]}] (* _G. C. Greubel_, Aug 12 2017 *)
%Y A130047 Cf. A007318, A034868, A048896, A133179.
%K A130047 nonn,tabf
%O A130047 0,1
%A A130047 _Philippe Deléham_, Oct 10 2007
%E A130047 Corrected by _N. J. A. Sloane_, Mar 22 2015 at the suggestion of Kevin Ryde