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A114213
A generalized Pascal triangle modulo 2.
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1
OFFSET
0,1
COMMENTS
Row sums are A114212. Diagonal sums are A114214.
Row sums of inverse are 0^n (conjecture).
LINKS
Jeffrey Shallit and Lukas Spiegelhofer, Continuants, run lengths, and Barry's modified Pascal triangle, arXiv:1710.06203 [math.CO], 2017.
FORMULA
T(n, k) = (Sum_{j=0..n-k} C(k, j)*C(n-k, j)*(1+(-1)^j)/2) mod 2.
EXAMPLE
Triangle begins
1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 1, 0, 1, 1;
1, 1, 0, 0, 1, 1;
1, 1, 1, 0, 1, 1, 1;
1, 1, 1, 1, 1, 1, 1, 1;
1, 1, 0, 1, 0, 1, 0, 1, 1;
1, 1, 0, 0, 0, 0, 0, 0, 1, 1;
1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1;
PROG
(PARI) T(n, k) = sum(j=0, n-k, binomial(k, j)*binomial(n-k, j)*(1+(-1)^j)/2) % 2; \\ Michel Marcus, Jun 06 2021
CROSSREFS
Sequence in context: A178788 A131217 A105567 * A108358 A267959 A144384
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Nov 17 2005
STATUS
approved