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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, 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;

CROSSREFS

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 21 19:17 EDT 2019. Contains 328308 sequences. (Running on oeis4.)