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A087748 Triangle formed by reading triangle of Stirling numbers of the first kind (A048994) mod 2. 3
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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

Table of n, a(n) for n=0..104.

Bill Gosper, Colored illustrations of triangle of Stirling numbers of first kind read mod 2, 3, 4, 5, 6, 7

FORMULA

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

EXAMPLE

Triangle begins:

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, 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, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1,

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1,

...

CROSSREFS

Cf. A008275, A008276, A048994, A087755.

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

Sequence in context: A189921 A167371 A127241 * A117446 A187034 A101688

Adjacent sequences:  A087745 A087746 A087747 * A087749 A087750 A087751

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Oct 02 2003

EXTENSIONS

Edited and extended by Henry Bottomley, Dec 01 2003

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)