A334636 Number of different values of (x_n, x_1*x_2*...*x_n) where x_1=1 and x_i-x_{i-1} is 0 or 1.

1, 2, 4, 8, 16, 31, 59, 110, 202, 366, 653, 1143, 1961, 3303, 5480, 8992, 14647, 23742, 38334, 61648, 98700, 157265, 249397, 393814, 619611, 971988, 1521015, 2374946, 3700290, 5751806, 8916890, 13780598, 21220014, 32540179, 49668909, 75435401

Offset: 1

Author

Jack Zhang, Sep 10 2020

Keywords

• nonn
• more

Crossrefs

Cf. A095684, A284001, A334635.

Programs

Python

k=[{(1, 1)}]
for i in range(20):
    k.append(set([(i[0]*i[1], i[1]) for i in k[-1]])|set([(i[0]*(i[1]+1), i[1]+1) for i in k[-1]]))
[len(i) for i in k]

Extensions

a(31)-a(36) from Bert Dobbelaere, Oct 19 2020