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A104974 A Fredholm-Rueppel triangle.

%I A104974 #17 Sep 08 2022 08:45:17
%S A104974 1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0,0,1,
%T A104974 0,1,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,1,0,0,0,1,0,1,0,0,
%U A104974 0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1
%N A104974 A Fredholm-Rueppel triangle.
%C A104974 Sequence matrix for A036987(n+1).
%C A104974 Riordan array ( (Sum_{k>=0} x^(2^k)/x^2) - 1/x, x).
%C A104974 Diagonal sums are A070939(n+1), with interpolated zeros.
%C A104974 Inverse is A104975.
%H A104974 G. C. Greubel, <a href="/A104974/b104974.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A104974 T(n, k) = A000108(n+1-k) mod 2. [Corrected by _R. J. Mathar_, Apr 21 2021]
%F A104974 Sum_{k=0..n} T(n, k) = A000523(n+1).
%e A104974 Triangle begins as:
%e A104974   1;
%e A104974   0, 1;
%e A104974   1, 0, 1;
%e A104974   0, 1, 0, 1;
%e A104974   0, 0, 1, 0, 1;
%e A104974   0, 0, 0, 1, 0, 1;
%e A104974   1, 0, 0, 0, 1, 0, 1;
%e A104974   0, 1, 0, 0, 0, 1, 0, 1;
%e A104974   0, 0, 1, 0, 0, 0, 1, 0, 1;
%e A104974   0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
%e A104974   0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
%e A104974   0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
%e A104974   0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
%e A104974   0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
%p A104974 A104974 := proc(n,k)
%p A104974     modp(A000108(n+1-k),2);
%p A104974 end proc:
%p A104974 seq(seq( A104974(n,k), k=0..n), n=0..15); # _R. J. Mathar_, Apr 21 2021
%t A104974 Table[Mod[CatalanNumber[n-k+1], 2], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jun 08 2021 *)
%o A104974 (Magma) [(Catalan(n-k+1) mod 2): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Jun 08 2021
%o A104974 (Sage) flatten([[mod(catalan_number(n-k+1), 2) for k in (0..n)] for n in (0..15)]) # _G. C. Greubel_, Jun 08 2021
%Y A104974 Cf. A000523 (row sums), A036987, A070939, A104975.
%K A104974 easy,nonn,tabl
%O A104974 0,1
%A A104974 _Paul Barry_, Mar 30 2005