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%I #6 Aug 05 2021 07:18:02
%S 9,12,15,17,18,20,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
%T 39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
%U 62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80
%N Numbers that are the sum of nine squares in one or more ways.
%H Sean A. Irvine, <a href="/A345498/b345498.txt">Table of n, a(n) for n = 1..1000</a>
%e 12 is a term because 12 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2.
%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, 9):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 1])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A003332, A345488, A345499, A345508.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 19 2021
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