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A280321
Number of 2 X 2 matrices with all elements in {0,..,n} having determinant = n*permanent.
3
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
OFFSET
0,2
COMMENTS
Same as A016754, except for n=1. Here a(1)=12 but A016754(1)=9.
LINKS
FORMULA
a(n+1) = (((n-2)*a(n))/(n-1)) + ((12*(n)^2-12*(n)+1)/(n-1)) for n>=1.
Conjectures from Colin Barker, Jan 01 2017: (Start)
a(n) = (1 + 2*n)^2 = A273789(n) = A273743(n) 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)
PROG
(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)))
CROSSREFS
Cf. A016754.
Sequence in context: A224669 A164577 A195143 * A198274 A229447 A175523
KEYWORD
nonn
AUTHOR
Indranil Ghosh, Jan 01 2017
STATUS
approved