A087755 Triangle read by rows: Stirling numbers of the first kind (A008275) mod 2.

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

Offset

1,1

Comments

Essentially also parity of Mitrinovic's triangles A049458, A049460, A051339, A051380.

References

Das, Sajal K., Joydeep Ghosh, and Narsingh Deo. "Stirling networks: a versatile combinatorial topology for multiprocessor systems." Discrete applied mathematics 37 (1992): 119-146. See p. 122. - N. J. A. Sloane, Nov 20 2014

Links

Table of n, a(n) for n=1..105.

Formula

T(n, k) = A087748(n, k) = A008275(n, k) mod 2 = A047999([n/2], k-[(n+1)/ 2]) = T(n-2, k-2) XOR T(n-2, k-1) with T(1, 1) = T(2, 1) = T(2, 2) = 1; 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
1 1
0 1 1
0 1 0 1
0 0 1 0 1
0 0 1 1 1 1
0 0 0 1 1 1 1
0 0 0 1 0 0 0 1
0 0 0 0 1 0 0 0 1
0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 1 0 1 0 1 0 1
0 0 0 0 0 0 1 0 1 0 1 0 1
0 0 0 0 0 0 1 1 1 1 1 1 1 1

Prog

(PARI) p = 2; s=14; S1T = matrix(s, s, n, k, if(k==1, (-1)^(n-1)*(n-1)!)); for(n=2, s, for(k=2, n, S1T[n, k]=-(n-1)*S1T[n-1, k]+S1T[n-1, k-1]));
S1TMP = matrix(s, s, n, k, S1T[n, k]%p);
for(n=1, s, for(k=1, n, print1(S1TMP[n, k], " ")); print()) /* Gerald McGarvey, Oct 17 2009 */

Crossrefs

Sequence in context: A118274 A275737 A080909 * A050072 A267576 A156707

Adjacent sequences: A087752 A087753 A087754 * A087756 A087757 A087758

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Oct 02 2003

Extensions

Edited and extended by Henry Bottomley, Dec 01 2003

Status

approved