A377122 Number of subsets of the first n nonzero decimal palindromes whose sum is a nonzero decimal palindrome.

1, 3, 7, 14, 23, 31, 40, 54, 78, 125, 219, 416, 865, 1719, 3375, 6646, 13139, 26103, 52029, 103989, 207805, 415509, 828997, 1629345, 3084165, 5525120, 9319815, 14896533, 22847075, 34326110, 51747646, 80304059, 130836329, 225170322, 406349931, 759326388, 1453773251

Offset: 1

Author

Ilya Gutkovskiy, Oct 17 2024

Keywords

• nonn
• base

Examples

			a(5) = 23 subsets: {1}, {2}, {3}, {4}, {5}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 5}, {4, 5}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {2, 3, 4}, {2, 4, 5} and {1, 2, 3, 5}.
		

Crossrefs

Cf. A002113, A339507.

Programs

Python

from functools import cache
def cond(s): return s > 0 and (w:=str(s)) == w[::-1]
def u(n): return A002113(n+1) # uses function in A002113
@cache
def b(n, s):
    if n == 0: return int(cond(s))
    return b(n-1, s) + b(n-1, s+u(n))
a = lambda n: b(n, 0)
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Oct 18 2024

Extensions

a(23) and beyond from Michael S. Branicky, Oct 18 2024