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

1,2

Links

Table of n, a(n) for n=1..37.

Example

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}.

Prog

(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

Crossrefs

Cf. A002113, A339507.

Sequence in context: A331240 A146931 A176675 * A213077 A294400 A115285

Adjacent sequences: A377119 A377120 A377121 * A377123 A377124 A377125

Keyword

nonn,base

Author

Ilya Gutkovskiy, Oct 17 2024

Extensions

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

Status

approved