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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are A114212. Diagonal sums are A114214.

Row sums of inverse are 0^n (conjecture).

LINKS

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

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

Cf. A114212, A114214.

Sequence in context: A178788 A131217 A105567 * A108358 A267959 A144384

Adjacent sequences:  A114210 A114211 A114212 * A114214 A114215 A114216

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 17 2005

STATUS

approved

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Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)