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

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, 10, 12, 13, 8, 13, 14, 11, 14, 14, 12, 15, 16, 12, 16, 18, 14, 18, 18, 14, 20, 20, 14, 19, 20, 16, 21, 24, 19, 21, 24, 18, 23, 24, 20, 24, 27, 23, 26, 25, 20, 29, 30, 23, 25, 31, 26

Offset: 0

Author

Philippe Deléham, Sep 03 2005

Keywords

• nonn

Comments

a(n) is also the number of ways of writing n as a sum of 5 triangular numbers (A000217). - Kenny Lau, Jul 05 2016

Links

• Kenny Lau, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A004770.

Programs

Python

f = open('b110534.txt', 'w')
N = 20000
n = 1
t = [0]  #triangular numbers
while t[-1] <= N:
    t += [t[-1]+n]
    n += 1
t = t[:-1]
a = [0]*(N+1)  #the sequence
length = len(t)
for i in range(length):
    for j in range(i,length):
        p = t[i] + t[j]
        if p > N: continue
        for k in range(j,length):
            q = p + t[k]
            if q > N: continue
            for l in range(k,length):
                r = q + t[l]
                if r > N: continue
                for m in range(l,length):
                    s = r + t[m]
                    if s > N: break
                    else: a[s] += 1
for index,value in enumerate(a):
    f.write(str(index)+" "+str(value)+"\n")
f.close()
# Kenny Lau, Jul 05 2016

Extensions

More terms from Don Reble, Sep 17 2005