Michael Mays - cp's OEIS frontend

User: Michael Mays

Michael Mays has authored 2 sequences.

A372768 The number of shaded cells in all compositions of n when light shines from the northwest. Here compositions are represented by stacked columns of adjacent cells.

0, 1, 4, 13, 34, 85, 199, 454, 1011, 2220, 4813, 10351, 22104, 46948, 99266, 209113

Offset: 1

Michael Mays, May 12 2024

			For n=4, the composition 1+3 produces 3 shaded cells, 2+2 produces 1, 3+1 produces 2, 1+1+2 produces 1, 4 produces 6, and the others have no shaded cells, for a total of 13, so a(4) = 13.

A. Blecher, A. Knopfmacher, and M. E. Mays, Shade in compositions of integers, Journal of Integer Sequences, Vol. 27 (2024), Article 24.5.6.

Cf. A366157.

A335296 Least index a(n) such that the sequences b(n,m) from A334539 are purely periodic after a(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 16, 24, 70, 31, 98, 112, 116, 170, 216, 488, 2012, 795, 328, 219, 2993, 4486, 1555, 814, 3575, 12296, 18386, 29659, 13665, 2162, 47685, 52346, 69061, 447927, 472933, 33798, 857812, 179171, 47447, 1195784, 332172, 618783, 248092, 3947618, 2718980, 15924182, 2857983, 3536883, 8606700

Offset: 1

Elad Michael, May 30 2020

nonn

By the pigeonhole principle, a(n) is upper bounded by n^n - n.

			The sequence b(3, m) is 1, 1, 2, 1, 2, 2, 2, 3, 1, 1, 2, ... which is periodic at index 1 with period 8.
The sequence b(8, m) is 1, 1, 2, 1, 3, 1, 4, ... 3, 4, 1, 2, 3, 3, 4, 2, 2, 3, 3, 4, 2, 3, 3, 4, 2, 2, 3, 3, ... which is periodic at index 24 with period 9.

Elad Michael, Table of n, a(n) for n = 1..100
Reddit user supermac30, Foggy Sequences.

Cf. A334539.

def a(n):
    b = [1];
    for i in range(2,n+1):
        b.append(b.count(b[-1]));
    prev = {tuple(b):1};
    m = 1;
    while(True):
        b.append(b.count(b[-1]));
        del b[0];
        m += 1;
        if(tuple(b) in prev):
            return prev[tuple(b)]
        else:
            prev[tuple(b)] = m;

cp's OEIS Frontend

User: Michael Mays

A372768 The number of shaded cells in all compositions of n when light shines from the northwest. Here compositions are represented by stacked columns of adjacent cells.

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