cp's OEIS Frontend

A345486 Numbers that are the sum of seven squares in nine or more ways.

%I A345486 #10 Jan 06 2024 09:23:26
%S A345486 69,70,78,79,81,82,85,87,88,90,91,93,94,95,96,97,98,99,100,101,102,
%T A345486 103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
%U A345486 120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136
%N A345486 Numbers that are the sum of seven squares in nine or more ways.
%H A345486 Sean A. Irvine, <a href="/A345486/b345486.txt">Table of n, a(n) for n = 1..1000</a>
%F A345486 Conjectures from _Chai Wah Wu_, Jan 05 2024: (Start)
%F A345486 a(n) = 2*a(n-1) - a(n-2) for n > 13.
%F A345486 G.f.: x*(-x^12 + x^11 - x^10 + x^9 - x^8 - x^7 + 2*x^6 - x^5 + x^4 - 7*x^3 + 7*x^2 - 68*x + 69)/(x - 1)^2. (End)
%e A345486 70 is a term because 70 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 8^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 7^2 = 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 5^2 + 5^2 = 1^2 + 1^2 + 2^2 + 4^2 + 4^2 + 4^2 + 4^2 = 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 4^2 + 5^2 = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 7^2 = 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 4^2 + 5^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 5^2 + 5^2 = 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 6^2 = 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 4^2.
%o A345486 (Python)
%o A345486 from itertools import combinations_with_replacement as cwr
%o A345486 from collections import defaultdict
%o A345486 keep = defaultdict(lambda: 0)
%o A345486 power_terms = [x**2 for x in range(1, 1000)]
%o A345486 for pos in cwr(power_terms, 7):
%o A345486     tot = sum(pos)
%o A345486     keep[tot] += 1
%o A345486     rets = sorted([k for k, v in keep.items() if v >= 9])
%o A345486     for x in range(len(rets)):
%o A345486         print(rets[x])
%Y A345486 Cf. A345476, A345485, A345487, A345496, A345527.
%K A345486 nonn
%O A345486 1,1
%A A345486 _David Consiglio, Jr._, Jun 20 2021