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A106465 A number triangle of GCDs mod 2. 5
1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Rows alternate between all 1's and alternating 1's and 0's. A 'mixed' sequence array: rows alternate between the rows of the sequence array for the all 1's sequence and the sequence array for the sequence 1,0,1,0,... Column 2k has g.f. x^2k/(1-x); column 2k+1 has g.f. x^(2k+1)/(1-x^2). Row sums are A029578(n+2). Antidiagonal sums are A106466.

This triangle is the Kronecker product of an infinite lower triangular matrix filled with 1's with a 2 X 2 lower triangular matrix of 1's. - Christopher Cormier, Sep 24 2017

LINKS

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

FORMULA

Number triangle T(n, k) = gcd(n-k+1, k+1) mod 2 if 1 <= k <= n, 0 otherwise;

T(n, k) = A003989(n, k) mod 2.

EXAMPLE

The triangle begins:

  n\k| 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ...

  ---+------------------------------------------------

   1 | 1

   2 | 1  1

   3 | 1  0  1

   4 | 1  1  1  1

   5 | 1  0  1  0  1

   6 | 1  1  1  1  1  1

   7 | 1  0  1  0  1  0  1

   8 | 1  1  1  1  1  1  1  1

   9 | 1  0  1  0  1  0  1  0  1

  10 | 1  1  1  1  1  1  1  1  1  1

  11 | 1  0  1  0  1  0  1  0  1  0  1

  12 | 1  1  1  1  1  1  1  1  1  1  1  1

  13 | 1  0  1  0  1  0  1  0  1  0  1  0  1

  14 | 1  1  1  1  1  1  1  1  1  1  1  1  1  1

  15 | 1  0  1  0  1  0  1  0  1  0  1  0  1  0  1

  ---+------------------------------------------------

  n\k| 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ...

... Reformatted by Wolfdieter Lang, May 12 2018

MATHEMATICA

Table[Boole@ OddQ@ GCD[n - k + 1, k], {n, 16}, {k, n}] // Flatten (* or *) Array[If[OddQ@ #, Boole@ OddQ@ Range@ #, ConstantArray[1, #]] &, 16] (* Michael De Vlieger, Sep 25 2017 *)

CROSSREFS

Cf. A003989, A029578, A106466.

Sequence in context: A054431 A164381 A106470 * A071027 A099990 A089939

Adjacent sequences:  A106462 A106463 A106464 * A106466 A106467 A106468

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, May 03 2005

STATUS

approved

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Last modified March 26 21:01 EDT 2019. Contains 321535 sequences. (Running on oeis4.)