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A280321
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Number of 2 X 2 matrices with all elements in {0,..,n} having determinant = n*permanent.
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3
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1, 12, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2025, 2209, 2401, 2601, 2809, 3025, 3249, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241, 6561, 6889, 7225, 7569, 7921, 8281, 8649, 9025, 9409, 9801, 10201
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n+1) = (((n-2)*a(n))/(n-1)) + ((12*(n)^2-12*(n)+1)/(n-1)) for n>=1.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
G.f.: (1 + 9*x - 8*x^2 + 9*x^3 - 3*x^4) / (1 - x)^3.
(End)
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PROG
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(Python)
def t(n):
s=0
for a in range(n+1):
for b in range(n+1):
for c in range(n+1):
for d in range(n+1):
if (a*d-b*c)==n*(a*d+b*c):
s+=1
return s
for i in range(41):
print(str(i)+" "+str(t(i)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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