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A087755 Triangle read by rows: Stirling numbers of the first kind (A008275) mod 2. 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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)