A075496 a(1)=1, a(n) = Sum_{k=1..n-1} max(a(k), a(n-k)).

1, 1, 2, 5, 14, 40, 118, 349, 1042, 3112, 9322, 27926, 83738, 251096, 753170, 2259161, 6777134, 20330360, 60990038, 182967002, 548897894, 1646684360, 4940043758, 14820103348, 44460282118, 133380762616, 400142204110, 1200426361234, 3601278832606, 10803835744648

Offset: 1

Author

Benoit Cloitre, Jan 11 2003

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A075535.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 1,
       add(max(a(k), a(n-k)), k=1..n-1))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Jan 08 2023

Formula

a(n) is asymptotic to c*3^n where c=0.05247353240352723607883446992217693404861703471190473058997502846657554868....