cp's OEIS Frontend

A345503 Numbers that are the sum of nine squares in six or more ways.

%I A345503 #15 Apr 26 2024 09:43:04
%S A345503 48,56,57,59,60,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,
%T A345503 81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
%U A345503 103,104,105,106,107,108,109,110,111,112,113,114,115,116,117
%N A345503 Numbers that are the sum of nine squares in six or more ways.
%C A345503 Numbers n such that A025433(n) >= 6. - _David A. Corneth_, Apr 26 2024
%H A345503 Sean A. Irvine, <a href="/A345503/b345503.txt">Table of n, a(n) for n = 1..1000</a>
%F A345503 Conjectures from _Chai Wah Wu_, Apr 25 2024: (Start)
%F A345503 a(n) = 2*a(n-1) - a(n-2) for n > 9.
%F A345503 G.f.: x*(-x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - 7*x^2 - 40*x + 48)/(x - 1)^2. (End)
%e A345503 56 is a term because 56 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 4^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 6^2 = 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 3^2 + 4^2 = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 3^2 + 4^2 + 4^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 5^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2.
%o A345503 (Python)
%o A345503 from itertools import combinations_with_replacement as cwr
%o A345503 from collections import defaultdict
%o A345503 keep = defaultdict(lambda: 0)
%o A345503 power_terms = [x**2 for x in range(1, 1000)]
%o A345503 for pos in cwr(power_terms, 9):
%o A345503     tot = sum(pos)
%o A345503     keep[tot] += 1
%o A345503     rets = sorted([k for k, v in keep.items() if v >= 6])
%o A345503     for x in range(len(rets)):
%o A345503         print(rets[x])
%Y A345503 Cf. A025433, A345493, A345502, A345504, A345545, A346805.
%K A345503 nonn
%O A345503 1,1
%A A345503 _David Consiglio, Jr._, Jun 20 2021