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A110534 Number of ways of writing 8n+5 as a sum of 5 odd squares.

%I A110534 #24 May 22 2025 10:21:35
%S A110534 1,1,1,2,2,2,3,3,2,4,4,3,5,5,4,6,6,4,7,7,5,8,8,7,9,9,6,10,10,8,11,11,
%T A110534 10,12,13,8,13,14,11,14,14,12,15,16,12,16,18,14,18,18,14,20,20,14,19,
%U A110534 20,16,21,24,19,21,24,18,23,24,20,24,27,23,26,25,20,29,30,23,25,31,26
%N A110534 Number of ways of writing 8n+5 as a sum of 5 odd squares.
%C A110534 a(n) is also the number of ways of writing n as a sum of 5 triangular numbers (A000217). - _Kenny Lau_, Jul 05 2016
%H A110534 Kenny Lau, <a href="/A110534/b110534.txt">Table of n, a(n) for n = 0..20000</a>
%o A110534 (Python)
%o A110534 f = open('b110534.txt', 'w')
%o A110534 N = 20000
%o A110534 n = 1
%o A110534 t = [0]  #triangular numbers
%o A110534 while t[-1] <= N:
%o A110534     t += [t[-1]+n]
%o A110534     n += 1
%o A110534 t = t[:-1]
%o A110534 a = [0]*(N+1)  #the sequence
%o A110534 length = len(t)
%o A110534 for i in range(length):
%o A110534     for j in range(i,length):
%o A110534         p = t[i] + t[j]
%o A110534         if p > N: continue
%o A110534         for k in range(j,length):
%o A110534             q = p + t[k]
%o A110534             if q > N: continue
%o A110534             for l in range(k,length):
%o A110534                 r = q + t[l]
%o A110534                 if r > N: continue
%o A110534                 for m in range(l,length):
%o A110534                     s = r + t[m]
%o A110534                     if s > N: break
%o A110534                     else: a[s] += 1
%o A110534 for index,value in enumerate(a):
%o A110534     f.write(str(index)+" "+str(value)+"\n")
%o A110534 f.close()
%o A110534 # _Kenny Lau_, Jul 05 2016
%Y A110534 Cf. A004770.
%K A110534 nonn
%O A110534 0,4
%A A110534 _Philippe Deléham_, Sep 03 2005
%E A110534 More terms from _Don Reble_, Sep 17 2005