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Triangle formed by reading triangle of Stirling numbers of the first kind (A048994) mod 2.
4

%I #17 Aug 09 2017 10:37:50

%S 1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,1,

%T 1,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,1,0,0,1,1,0,0,

%U 0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1

%N Triangle formed by reading triangle of Stirling numbers of the first kind (A048994) mod 2.

%D Brand, Neal; Das, Sajal; Jacob, Tom. The number of nonzero entries in recursively defined tables modulo primes. Proceedings of the Twenty-first Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1990). Congr. Numer. 78 (1990), 47--59. MR1140469 (92h:05004). - From _N. J. A. Sloane_, Jun 03 2012

%H Bill Gosper, <a href="/A008275/a008275.png">Colored illustrations of triangle of Stirling numbers of first kind read mod 2, 3, 4, 5, 6, 7</a>

%F T(n, k) = A087755(n, k) = A048994(n, k) mod 2 = A047999([n/2], k-[(n+1)/2]) = T(n-2, k-2) XOR T(n-2, k-1) with T(0, 0) = T(1, 1) = 1 and T(1, 0) = 0; T(2n, k) = T(2n-1, k-1) XOR T(2n-1, k); T(2n+1, k) = T(2n, k-1). - _Henry Bottomley_, Dec 01 2003

%e Triangle begins:

%e 1,

%e 0, 1,

%e 0, 1, 1,

%e 0, 0, 1, 1,

%e 0, 0, 1, 0, 1,

%e 0, 0, 0, 1, 0, 1,

%e 0, 0, 0, 1, 1, 1, 1,

%e 0, 0, 0, 0, 1, 1, 1, 1,

%e 0, 0, 0, 0, 1, 0, 0, 0, 1,

%e 0, 0, 0, 0, 0, 1, 0, 0, 0, 1,

%e 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1,

%e 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1,

%e 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1,

%e ...

%Y Cf. A008275, A008276, A048994, A087755.

%Y Also parity of triangles A049444, A049459, A051338, A051379, A051523.

%K easy,nonn,tabl

%O 0,1

%A _Philippe Deléham_, Oct 02 2003

%E Edited and extended by _Henry Bottomley_, Dec 01 2003