OFFSET
1,1
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..1000
FORMULA
Conjectures from Chai Wah Wu, Apr 25 2024: (Start)
a(n) = 2*a(n-1) - a(n-2) for n > 13.
G.f.: x*(-x^12 + x^11 - x^10 + x^9 - x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - 8*x^2 - 36*x + 45)/(x - 1)^2. (End)
EXAMPLE
54 = 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 4^2 + 5^2
= 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 6^2
= 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 3^2 + 4^2
= 1^2 + 2^2 + 2^2 + 2^2 + 3^2 + 4^2 + 4^2
= 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 5^2
so 54 is a term.
PROG
(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 5])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
David Consiglio, Jr., Jun 20 2021
STATUS
approved