A334635 Number of different values of x_1*x_2*...*x_n where x_1=1 and x_i-x_{i-1} is 0 or 1.

1, 2, 4, 8, 15, 28, 51, 92, 164, 286, 486, 808, 1322, 2142, 3456, 5571, 8975, 14427, 23094, 36766, 58201, 91675, 143841, 225045, 351321, 547393, 851160, 1320339, 2042195, 3147614, 4831237, 7380048, 11213838, 16942556, 25447992, 38000880

Offset

1,2

Comments

a(n) is also the number of different possible products of nesting levels in n pairs of parentheses.

Links

Table of n, a(n) for n=1..36.

Example

n=5: possible values are 1*1*1*1*1, 1*1*1*1*2, 1*1*1*2*2, 1*1*1*2*3, 1*1*2*2*2, 1*1*2*2*3, 1*1*2*3*3, 1*1*2*3*4, 1*2*2*2*2, 1*2*2*2*3, 1*2*2*3*3, 1*2*2*3*4, 1*2*3*3*3, 1*2*3*3*4, 1*2*3*4*4, 1*2*3*4*5, but since 1*1*2*3*4=1*2*2*2*3, there are only 15 different values.

Prog

(Python3)
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(set(j[0] for j in i)) for i in k]

Crossrefs

Sequence in context: A006727 A007673 A182725 * A358836 A029907 A005682

Adjacent sequences: A334632 A334633 A334634 * A334636 A334637 A334638

Keyword

nonn

Author

Jack Zhang, Sep 10 2020

Extensions

a(31)-a(32) from David A. Corneth, Sep 12 2020

a(33)-a(36) from Bert Dobbelaere, Oct 19 2020

Status

approved