A373688 a(n) is the number of ways n can be written as a sum of a practical number and two hexagonal numbers.

1, 2, 2, 2, 1, 2, 2, 4, 2, 2, 1, 2, 3, 3, 1, 3, 3, 5, 3, 4, 2, 4, 3, 4, 3, 2, 3, 3, 3, 6, 5, 6, 4, 5, 4, 7, 4, 4, 3, 5, 3, 6, 3, 5, 4, 6, 6, 7, 6, 4, 4, 6, 4, 6, 5, 4, 7, 7, 3, 6, 7, 7, 6, 7, 3, 8, 5, 7, 6, 7, 6, 8, 6, 7, 7, 8, 4, 8, 7, 6

Offset: 1

Author

Duc Van Khanh Tran, Jun 13 2024

Keywords

• nonn

Comments

Somu and Tran (2024) proved that a(n) > 0 for sufficiently large n and conjectured that a(n) > 0 for all n > 0. The conjecture was checked up to 10^8.

Links

• Duc Van Khanh Tran, Table of n, a(n) for n = 1..10000
• Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.

Crossrefs

Cf. A000384, A005153.