A341150 Triangle read by rows, lower triangle of the all-zeros matrix modified step by step with T(0,0) = 1, then at each step, if T(n,k) has changed in previous step, increase T(n+k,k) and T(3n+1-2k,2n+1-k) by 1.

1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1

Offset

0

Links

Table of n, a(n) for n=0..90.

Niccolò Castronuovo, On the number of fixed points of the map gamma, arXiv:2102.02739 [math.NT], 2021.

Example

Triangle begins:
  [1];
  [0, 1];
  [0, 1, 1];
  [0, 1, 0, 1];
  [0, 1, 1, 0, 1];
  [0, 1, 0, 0, 1, 1];
  [0, 1, 1, 1, 0, 0, 1].

Prog

(PARI) incr(m, nn, vincr) = if ((vincr[1]<nn) && (vincr[2]<nn), m[vincr[1]+1, vincr[2]+1]++); m;
tabl(nn) = {my(m = matrix(nn, nn), istep=0, vstep, nvstep); for (istep=0, nn, if (istep==0, vstep = [[0, 0]], vstep = nvstep); nvstep = List(); for (i=1, #vstep, my(step=vstep[i]); m = incr(m, nn, step); if (istep, listput(nvstep, [step[1]+step[2], step[2]])); listput(nvstep, [3*step[1]+1-2*step[2], 2*step[1]+1-step[2]]); ); ); m; }
out(nn) = my(m=tabl(nn)); for(i=1, nn, print(vector(i, k, m[i, k])); );

Crossrefs

Row sums give A341151.

Sequence in context: A287722 A284588 A113704 * A244220 A283963 A131670

Adjacent sequences: A341147 A341148 A341149 * A341151 A341152 A341153

Keyword

nonn,tabl

Author

Michel Marcus, Feb 06 2021

Status

approved