OFFSET
1,1
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
From Chai Wah Wu, May 09 2024: (Start)
All integers >= 24 are terms. Proof: since 5 can be written as the sum of 5 positive squares and any integer >= 34 can be written as a sum of 5 positive squares (see A025429), any integer >= 39 can be written as a sum of 10 positive squares. Integers from 24 to 38 are terms by inspection.
a(n) = 2*a(n-1) - a(n-2) for n > 9.
G.f.: x*(-x^8 + x^7 - x^6 + x^5 - x^4 - x^3 - 7*x + 10)/(x - 1)^2. (End)
EXAMPLE
13 is a term because 13 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2.
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, 10):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 1])
for x in range(len(rets)):
print(rets[x])
(Python)
def A345508(n): return (10, 13, 16, 18, 19, 21, 22)[n-1] if n<8 else n+16 # Chai Wah Wu, May 09 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
David Consiglio, Jr., Jun 19 2021
STATUS
approved