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A377123
Number of subsets of the first n nonzero triangular numbers whose sum is a nonzero triangular number.
3
1, 2, 4, 5, 8, 13, 18, 29, 48, 81, 136, 228, 420, 747, 1326, 2468, 4520, 8296, 15232, 28196, 52504, 96936, 181699, 340998, 640091, 1207386, 2282956, 4328536, 8211989, 15623003, 29787092, 56831499, 108591159, 207851120, 398222781, 763760138, 1466661416, 2819529654, 5425826011, 10450403468
OFFSET
1,2
EXAMPLE
a(5) = 8 subsets: {1}, {3}, {6}, {10}, {15}, {6, 15}, {1, 3, 6} and {3, 10, 15}.
PROG
(Python)
from math import isqrt
from functools import cache
def cond(s): k = 8*s+1; return s > 0 and isqrt(k)**2 == k
def u(n): return n*(n+1)//2
@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
Sequence in context: A327045 A395925 A288668 * A264800 A293189 A278695
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 17 2024
EXTENSIONS
a(23) and beyond from Michael S. Branicky, Oct 18 2024
STATUS
approved