A347316 Irregular triangle read by rows: T(n,k) = number of times k appears in n-th row of A342585, n >= 0..

1, 1, 2, 1, 0, 3, 1, 2, 1, 1, 1, 1, 1, 0, 0, 4, 1, 2, 1, 0, 1, 2, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 2, 0, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 0, 0, 2, 0, 2, 1, 1, 1, 2, 1, 1, 1

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10295 (rows 0 <= n <= 108, flattened)

Example

Triangle begins:
1,
1,2,
1,0,3,
1,2,1,1,1,
1,1,0,0,4,
1,2,1,0,1,2,1,
...
Row 4 of A342585 is [4, 4, 4, 1, 4, 0], containing one 0, one 1, and four 4's; so row 4 here is [1, 1, 0, 0, 4].

Mathematica

Block[{c, k, m, nn = 12}, c[0] = 1; Join[{{1}}, Map[Function[w, {1}~Join~Array[If[ListQ[#], Length[#], 0] &@ Lookup[w, #] &, Max@ Keys[w]]]@ KeySort@ PositionIndex[#] &, SplitBy[Reap[Do[k = 0; While[IntegerQ[c[k]], Set[m, c[k]]; Sow[m]; If[IntegerQ@ c[m], c[m]++, c[m] = 1]; k++]; Sow[0]; c[0]++, nn]][[-1, -1]], # == 0 &][[1 ;; -1 ;; 2]]]] ] // Flatten (* Michael De Vlieger, Oct 12 2021 *)

Crossrefs

Cf. A342585, A347299 (row sums).

Sequence in context: A333432 A333500 A182720 * A146540 A162922 A246180

Adjacent sequences: A347313 A347314 A347315 * A347317 A347318 A347319

Keyword

nonn,tabf

Author

N. J. A. Sloane, Sep 09 2021

Extensions

More terms from Alois P. Heinz, Sep 09 2021

Status

approved