A345483 - OEIS

%I #9 Apr 26 2024 03:20:36

%S 55,58,61,63,64,66,67,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,

%T 85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,

%U 106,107,108,109,110,111,112,113,114,115,116,117,118,119,120

%N Numbers that are the sum of seven squares in six or more ways.

%H Sean A. Irvine, <a href="/A345483/b345483.txt">Table of n, a(n) for n = 1..1000</a>

%F Conjectures from _Chai Wah Wu_, Apr 25 2024: (Start)

%F a(n) = 2*a(n-1) - a(n-2) for n > 9.

%F G.f.: x*(-x^8 + x^7 - x^6 + x^5 - x^4 - x^3 - 52*x + 55)/(x - 1)^2. (End)

%e 58 is a term because 58 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 7^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 6^2 = 1^2 + 1^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2 = 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2 = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2 = 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**2 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 7):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v >= 6])

%o     for x in range(len(rets)):

%o         print(rets[x])

%Y Cf. A344810, A345482, A345484, A345493, A345524.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021