|
| |
|
|
A280059
|
|
Number of 2 X 2 matrices having all elements in {-n,..,0,..,n} with determinant = permanent.
|
|
2
|
|
|
|
1, 45, 225, 637, 1377, 2541, 4225, 6525, 9537, 13357, 18081, 23805, 30625, 38637, 47937, 58621, 70785, 84525, 99937, 117117, 136161, 157165, 180225, 205437, 232897, 262701, 294945, 329725, 367137, 407277, 450241, 496125
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = 16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3 for n>0.
G.f.: (1 + 41*x + 51*x^2 + 3*x^3)/(1 - x)^4.
E.g.f.: (1 + 44*x + 68*x^2 + 16*x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
|
|
|
MATHEMATICA
|
Table[16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 45, 225, 637}, 50] (* G. C. Greubel, Dec 25 2016 *)
|
|
|
PROG
|
def t(n):
s=0
for a in range(-n, n+1):
for b in range(-n, n+1):
for c in range(-n, n+1):
for d in range(-n, n+1):
if (a*d-b*c)==(a*d+b*c):
s+=1
return s
for i in range(0, 1001):
print str(i)+" "+str(t(i))
(PARI) for(n=0, 50, print1(16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, ", ")) \\ G. C. Greubel, Dec 25 2016
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
